ADDIS ABABA UNIVERSITY

ADDIS ABABA INSTITUTE OF TECHNOLOGY

SCHOOL OF CIVIL AND ENVIRONMENTAL ENGINEERING

A Study on The Effect of Prying Action on the

Tension Resistance of Beam-to-Column
Connections
A Thesis in Structural Engineering

By Mihret Moges
May, 2019
Addis Ababa

A Thesis
Submitted in Partial Fulfillment of the Requirements for the Degree of Master of
Science
 ADDIS ABABA UNIVERSITY

ADDIS ABABA INSTITUTE OF TECHNOLOGY

SCHOOL OF CIVIL AND ENVIRONMENTAL ENGINEERING

“A Study on the Effect of Prying Action on the Tension Resistance of Beam-to-Column

Connections”

By
Mihret Moges

Approved by the Board of Examiners:

Dr. Abrham Gebre

Advisor Signature Date

Dr. Esayas G.yohannes

Internal Examiner Signature Date

Dr.-Ing. Girma Zerayohannes

External Examiner Signature Date

Dr. Henok Fikre

Dean, SCEE Signature Date

 UNDERTAKING

I certify that research work titled “A Study on the Effect of Prying Action on the
Tension Resistance of Beam-to-Column Connections” is my own work. The work has
not been presented elsewhere for assessment. Where material has been used from other
sources it has been properly acknowledged / referred.

Mihret Moges
Addis Ababa University Addis Ababa Institute of Technology

Acknowledgment

I would like to forward my deepest appreciation and gratitude to my advisor Abrham

Gebre (PhD) for his encouragement and constructive advice throughout the course of
the thesis.

I would also like to thank my friends and classmates for their support, encouragement and
assistance.

Last, but certainly not least, I would like to express my deepest gratitude to my family
especially my mother, W/o Mantegbosh Gebissa, for her unwavering love, support and
encouragement.

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TABLE OF CONTENTS

LIST OF FIGURES ......................................................................................................... V

LIST OF TABLES ......................................................................................................... VI

LIST OF SYMBOLS .................................................................................................... VII

ABSTRACT....................................................................................................................... 1

1. INTRODUCTION ..................................................................................................... 2

1.1 Background Information ...................................................................................... 2

1.2 Objective of the Research .................................................................................... 3
1.3 Statement of the Problem ..................................................................................... 3
1.4 Scope of the Research .......................................................................................... 3
1.5 Research Methodology ........................................................................................ 4
1.6 Organization of the Thesis ................................................................................... 4
2. LITRATURE REVIEW............................................................................................ 5

2.1. Prying Action ....................................................................................................... 5

2.1.1. Factors Affecting Prying Action ................................................................... 6

2.2. Previous Studies Done on Prying Action ............................................................. 7

2.3. Existing Expressions for Prying Action ............................................................. 13
2.4. Equivalent T-stub ............................................................................................... 18
3. MATERIALS AND METHOD OF ANALYSIS .................................................. 20

3.1. Study Parameters................................................................................................ 20

3.2. Finite Element Model......................................................................................... 22
3.2.1. Simplified Bolt............................................................................................ 23

3.2.2. Material data ............................................................................................... 23

3.3. Sampling Technique .......................................................................................... 24

3.3.1. Sensitivity Analysis .................................................................................... 25

4. ANALYSIS ............................................................................................................... 27

4.1. Validation of the Finite Element Model ............................................................ 27

4.2. Analytical Study of the Finite Element Model .................................................. 28
4.3. Prying Force Calculation ................................................................................... 29
4.4. Design Resistance According to ES EN 1993-1-8:2013 ................................... 30
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5. RESULTS AND DISCUSSION.............................................................................. 31

5.1. Evaluation of the Finite Element Models .......................................................... 31

5.2. Evaluation of the Design Tension Resistance in ES EN 1993-1-8:2013 ........... 40
6. CONCLUSION AND RECOMMENDATIONS .................................................. 42

6.1. Conclusion ......................................................................................................... 42

6.2. Recommendation ............................................................................................... 43
REFERENCES ............................................................................................................... 44

APPENDICES ................................................................................................................. 45

Appendix A ................................................................................................................... 45
Appendix B ................................................................................................................... 46
Appendix C ................................................................................................................... 47
Appendix D ................................................................................................................... 48

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List of Figures
Figure 2-1 Schematic of joint deformation ......................................................................... 5
Figure 2-2 T-stub connection.............................................................................................. 5
Figure 2-3 Bending of the T-stub flange ............................................................................ 6
Figure 2-4 Force distribution in the T-stub......................................................................... 6
Figure 2-5 T-stub analogy for extended endplates ............................................................. 7
Figure 2-6 Simplified prying model of Douty and McGuire [9] ........................................ 9
Figure 2-7 Kennedy’s split-tee model .............................................................................. 11
Figure 2-8 Flange behavior models .................................................................................. 11
Figure 2-9 Model for determining the prying force, Q ..................................................... 13
Figure 2-10 Prying force on a T-stub ............................................................................... 13
Figure 2-11 Prying Force according to the Chinese code ................................................. 14
Figure 2-12 Combined prying force and tension according to the Indian standard ......... 16
Figure 2-13 T-stub geometry ............................................................................................ 18
Figure 2-14 Dimensions of an equivalent T-stub flange .................................................. 19
Figure 3-1 Constitutive model for T-stub and bolt ........................................................... 22
Figure 3-2 Assembled model and simplified bolt............................................................. 22
Figure 4-1 Comparison of FEM and experimental result ................................................. 27
Figure 5-1 Load-deflection curve of configuration 4 ....................................................... 31
Figure 5-2 T-stub stress at 129.6kN ................................................................................. 32
Figure 5-3 Bolt and T-stub stresses at 279.9kN ............................................................... 32
Figure 5-4 Bolt Vs. Applied force for configuration 4 ..................................................... 33
Figure 5-5 Load-deflection curve of configuration 8 ....................................................... 33
Figure 5-6 T-stub stress at 131.098kN ............................................................................. 34
Figure 5-7 Bolt and T-stub stresses at 280.8kN ............................................................... 34
Figure 5-8 Bolt Vs. Applied force for configuration 8 ..................................................... 35
Figure 5-9 Load-deflection curve of configuration 13 ..................................................... 35
Figure 5-10 T-stub stress at 424.5kN ............................................................................... 36
Figure 5-11 Bolt and T-stub stresses at 460.614kN ......................................................... 36
Figure 5-12 Bolt Vs. Applied force for configuration 13 ................................................. 36
Figure 5-13 Contact criteria for prying action .................................................................. 38
Figure 5-14 Sensitivity analysis for the finite element model .......................................... 39
Figure 5-15 Sensitivity Analysis for prying force ............................................................ 40
Figure 5-16 Sensitivity analysis for ES EN 3:1-8 ............................................................ 41

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List of Tables
Table 3-1 Mechanical properties of flange ....................................................................... 20
Table 3-2 Mechanical properties of bolt ........................................................................... 20
Table 3-3 End plate thickness ........................................................................................... 21
Table 3-4 Values for n and m ........................................................................................... 21
Table 3-5 Values of the independent variables................................................................. 21
Table 3-6 Material data for FEM ...................................................................................... 23
Table 3-7 Statistical variation of random variables .......................................................... 24
Table 3-8 Configurations used.......................................................................................... 24
Table 4-1 Material data for validation .............................................................................. 27
Table 4-2 Effective length calculations ............................................................................ 30
Table 5-1 Prying force calculation ................................................................................... 37
Table 5-2 Sensitivity Analysis parameters for FEM ........................................................ 39
Table 5-3 Sensitivity Analysis parameters for prying action ........................................... 39
Table 5-4 Sensitivity Analysis parameters for ES EN 3:1-8 ............................................ 40

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List of Symbols

The following symbols are used in this paper.

αi = Sensitivity factor

As = Tensile stress area

B = Bolt force

Bo = Additional bolt force due to prying force

C.V = Coefficient of variation

Ft,Rd = Tensile strength of a single bolt

FT,Rd = design tension resistance of a T-stub flange

fyb = yield strength of the bolt

fyp = yield strength of the end-plate

leff = effective length

m = distance between bolt axis and root of the profile

n = distance between bolt axis and edge of the end-plate

Q = Prying Force

Qall = Allowable prying Force

tf = thickness of the flange

T = Applied Tension force

Ui = Uncertainty coefficient

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ABSTRACT

The effect of prying action in endplates tends to increase the tensile load that is transferred
to the bolts and therefore its effect should be evaluated. The aim of this thesis is to study
the effect of prying action on the tension resistance of beam-to-column connections and
the scope was restricted to end plate connections for which the collapse was governed by
the tension zone idealized by T-stubs. Where there is deformation, no matter how small,
there is bound to be a prying force created. The question is whether or not the connection
fails because of it. And this is based on the capacity of the bolts to carry the additional
force and the capacity of the flange to not form a mechanism and fail. 30 finite element
models were modeled and studied to study the effects of four variables on the generation
and amount of prying force. From this analysis, it was found that the thickness of the
flange, yield strength of the bolt, yield strength of the flange and the distance between the
bolt axis and the root of the profile have a -43%, 37%, -4% and 16% contributions to the
prying force generated. It was found that for thin flanges, using low yield strength bolts
resulted in lower prying force than using high yield strength bolts and for thick flanges,
using high yield strength bolts resulted in higher prying force generation than those with
lower yield strength bolts whose prying forces were minimums, even zero. The studies
also revealed that the best and optional combination to yield a minimum, even nonexistent,
prying force and minimum deformation were thick flanges with low yield strength bolts.

Key Words: T-stub, Tension Resistance, Prying Force

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1. INTRODUCTION

1.1 Background Information

Steel has become one of the most popular construction materials for both low and high rise
buildings and for truss structures, and its structural properties such as high strength-to-
weight ratio and ductility, offer distinct advantages when compared to concrete. Fast
erection speed, long spans, elegance and adaptability are other features which makes steel
a popular structural material.

The behavior of a structure is influenced as much by the behavior of its joints as by the
behavior of its individual members. One of the design requirements aside from its
effectiveness and economy is the harmony within the structure which is affected by the
relationships between the different systems of the structure. This leads to the question of
the effectiveness of the connections and their load carrying capacity. ES EN 1993-1-
8:2013 hereafter referred to as ES EN 3:1-8, provides the necessary procedures for the
design of these connections. This code along with others considers the effect of prying
forces, which is the force within a connection which is resulted from the deformation of
the connected parts, when designing bolts.

Bolted connections under tensile force are liable to be fractured under strength lower than
the estimated design strength due to prying action between members. Thus, there have
been many studies on estimating such prying forces between members. Prying action is a
phenomenon that results in an additional tension on fasteners due to the deformation of t-
stub flanges when loaded. Extensive studies on the subject of prying action have been
carried out and they all have concluded that there can exists a failure in the flange, plastic
hinge formations, in addition to a failure in the bolts and that the stiffness properties of
both the flange and the fasteners are significant determinants of this effect.

This research paper studied the effect of prying action on the tensile resistance of an end-
plate beam-to-column connection varying the thickness of the flange, the distance between
bolt axis and root of the profile, yield strength of the plate, and yield strength of the bolt.

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1.2 Objective of the Research

General objective: to study the prying forces generated and failure mechanisms of
connections.
Specific objectives:
 To study the effect of thickness of the flange, the distance between bolt axis
and root of the profile, yield strength of the plate, and yield strength of the bolt
on prying action.
 To evaluate the performance of the design tension resistance of a t-stub flange
given in ES EN 3:1-8, 6.2.4.1 (5)

1.3 Statement of the Problem

ES EN 3:1-8, 6.2.4 has given the design tension resistance of a t-stub flange. However,
the effect of prying force on the behavior of the flange is not clearly outlined in the
article. Moreover, the design industry is not giving attention to the effect of prying
action on bolts and plates which could lead the connection to failure. Generally, the
fact that prying force can drastically increase the amount of tensile stress produced in
the bolt, and possibly cause failure in the flange plate itself is the driving force for this
research in studying the various variables affecting this action.

1.4 Scope of the Research

This research is limited to the study of prying action on the tensile resistance of beam-
to-column connections when subjected to a tensile load. In this research, the effect of
bolt pre-loading, bolt position and spacing on prying action are not considered.

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1.5 Research Methodology

Dependent variables: prying force

Independent variables: thickness of the flange, tf, the distance between bolt axis and root
of the profile, m, yield strength of the plate, fyp and yield strength of the bolt, fyb
Extraneous variables: bolt diameter, effective length of the flange, thickness of the web
of the flange, number of bolts.
The following procedures were followed:

1. A beam-to-column connection and a tension member connection were modeled

and simulated using available simulation software, ABAQUS
2. The failure of the connection in each simulation were studied based on failure
mechanism and value of prying force generated,
3. The effect of the independent variables on the prying action were thoroughly
investigated,
4. The design tension resistance of a t-stub flange was checked.

1.6 Organization of the Thesis

The thesis consists of an introduction, four chapters and general conclusions. A general
introduction, scope and objective of the research are discussed in the first chapter. The
second chapter provides a review of relevant literatures on prying action. Furthermore
previous studies and existing expressions for prying forces are reviewed.

The third chapter presents the mechanical properties of materials used in the calculations
and for the finite element models as well as the sampling technique used. The fourth
chapter presents the method of analysis which involves the validation of the finite element
models, and the method of analysis used.

The fifth chapter presents the results and discussion of the results obtained from the
models. Whereas the sixth chapter presents the general conclusion and recommendations
made for future works.

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2. LITRATURE REVIEW

2.1. Prying Action

Depending on the direction of the bending moment, either the top or bottom flange T-stub
in a beam-to-column connection is stressed in tension. The flexural deformation of the
connected plates due to the exerted tension force results in an increased fastener/bolt
forces. Depending on the flexural rigidity of the T-stub, additional forces may be
developed near the flange tip; this phenomenon is referred as prying action and is
illustrated in Figure 2.1[4].

Figure 2-1 Schematic of joint deformation

An applied load of 2T on the less complicated and simplified connection in Figure 2.2 is
to be transmitted. At first glance it might seem that each bolt in this connection will
transmit a load 2T/2=T but in practice, the applied external load will bend the T-stub flange
(see Figure 2.3). This deflection will cause the flanges to exert pressure on each other.
The result is that the bolts must not only transmit the external load 2T but also the internal
loads Q which develop due to the deflection of the flanges, as illustrated in Figure 2.4 [10].

Figure 2-2 T-stub connection

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Figure 2-3 Bending of the T-stub flange

`

Figure 2-4 Force distribution in the T-stub

Initially, the external load reduces the contact pressure between the flanges until separation
at the bolt line occurs. Bending in the outer portion of the flanges develops prying forces
acting between the bolt line and the edge of the flanges. These forces will develop only
when the ends of the flanges are in contact due to the external load [4].

2.1.1. Factors Affecting Prying Action

Although every component has an effect on the strength and stiffness of a connection,
different researchers have studied specific components to evaluate their effect on the
overall resistance.

Munse, Peterson and Chesson studied the effect of tee-section flange thickness and the
grip length of the bolts and found that changes in the flanges thickness resulted in a range
of bolt efficiency of 30% in the connections tested, connections with thicker flanges
yielding higher efficiency. The effect of grip length was found to be small [11].

Douty and McGuire varied the flange thickness, the edge distance and the bolt diameter
and came up with a semi-empirical equation to calculate the prying force created. While
Leahey and Munse studied the effect of bolt pretension the behavior of the connection and
found that changes in bolt pretension has little effect on the ultimate load of the connection
when subjected to a static load [11].

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Surtees and Mann also concluded that the bolt pretension has little effect on the connection
stiffness and suggested an increase of 33% in the direct bolt tensile force to account for
the prying forces. Salem, Sayed-Ahmed and Samaan studied the effect of bolt diameter,
bolt end distance and end plate thickness and concluded that large edge distances decrease
the bending moment capacity, and prying force to tensile bolt force ratio decreases by the
increase in head plate thickness. For specimens with thick head plates, the prying force
vanishes completely [1].

In this research, the effect of the end plate thickness, the distance between bolt axis and
root of the profile, yield strength of the plate, and yield strength of the bolt are studied.

2.2. Previous Studies Done on Prying Action

Many researches are based on an analogy between the extended region of the endplate and
tee-stubs, since it is easier to conceptualize and estimate prying action with tee-stubs.
Previous investigations done on prying action on Beam-to-column and t-stub connections
are reviewed in this section.

The tension region of a beam-column connection can be idealized as a tee-stub. Figure 2.5
show the enlarged view of the tee-stub in flexure under load where 2F is the flange force,
Q is the prying force, and P is the bolt force. The extended region of the endplate, or/and
the column flange in the tension region, is considered to behave like a tee profile with bolts
placed around the stem [6].

Figure 2-5 T-stub analogy for extended endplates

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There were researchers like Surtees and Mann who tried to model endplate connections
directly, and who conceptualized the extended regions of the endplate as half of a fixed
ended beam terminating at the bolt line. On the other hand, there were researchers like
Nair, Birkemoe and Munse, who concentrated more on tee-stubs and the tee-stub analogy,
and who tended to conceptualize this as a simply supported beam extended to the edge of
the plate. The former group of researchers tended to ignore prying forces or to asses them
using simple rule of thumbs, while the latter group went to considerable trouble to calculate
the prying forces on tee-stubs. The prying action assumptions for tee-stubs were then
‘extrapolated’ to extended endplates [6].

Douty and McGuire

Douty and McGuire’s prying force derivation was involved, based on the initial elastic
deformation of the endplate around the bolts due to the bolt pretension, and also including
the initial bolt elongations. Their analytical model was derived from the assumption that
the tee flange behaves as a simply supported elastic beam, spanning across the flange ends.
The development of the prying force equation, relating the prying force Q to the ultimate
load of the connection, was based on both equilibrium and compatibility conditions. The
semi-empirical equation developed by Douty and McGuire that is based on the assumption
that prying forces act at the tip of the flange  [6]
1 is: wt 4 
  2  
2  30ab Ab 
Q T
 a  a    wt 4  
    1   
 b  3b    6ab Ab  
2

(2-1)
Where: w = width of the flange,

t = thickness of the flange,

a = distance from face of the stem to the centerline of the bolt,

b = distance from the centerline of the bolt to the edge of the flange,

Ab = area of the bolt,

Q = prying force, and

T = external applied force.

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However, the above equation is based on a specific combination of the bolt and plate
material, different formulas maybe required for different bolt and plate combinations.

Figure 2-6 Simplified prying model of Douty and McGuire [9]

Surtees and Mann

Surtees and Mann tested six single-sided extended endplate connections with variable
endplate thickness and proposed equations for obtaining the endplate thickness and the
bolt sizes. The resulting equationMfor
p the endplate thickness is:
tp 
 2b p d f 
16d f   
 1
p p 2 
(2-2)

Where df is the depth between centers of the beam flanges, p2 is the bolt gauge distance,
p1 is the bolt pitch distance, and bp is the endplate width. They considered the possibility
of prying action, catering for this with an empirical 30% increase in the bolt load. Thus,
the bolts are to be sized for a force P, where: [6]
Mp Mp
P * 1.3 
4d f 3d f
(2-3)

Nair, Birkemoe and Munse

In their study to determine the behavior of high strength bolts loaded in direct tension in
tee-connections, Nair, Birkemoe and Munse concluded that the geometry of the tee-
sections, the size of the bolts and the bolt type, in their case ASTM A325 & A490, govern
the magnitude of the prying force. This study is based on bolt failure as the critical failure

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mode. The ratio of the prying force, Q, to the externally applied load, p, in a bolted tee-
connection at the point of failure of the bolts can be accurately determined by means of
the equations shown below [11].

For connections with A325 bolts

 Q  100bd  18wt
2 2
   0
 P u 70ad  21wt
2 2
(2-4)

For connections with A490 bolts

 Q  100bd  14wt
2 2
   0
 P u 62ad  21wt
2 2
(2-5)

Where: d = nominal bolt diameter,

t = thickness of the tee-section flange,

w= length of flange tributary to each bolt,

b = distance from the bolt line to the face of the web minus 1/16 inch,

a = distance from the blot line to the edge of the flange (a≤2t)

The ultimate load, Pu, of a tee-connection which fails by bolt fracture may be determined
from the equation, nTu
Pu 
Q
1  
 P u (2-6)

Where: n = number of bolts in the connection,

Tu = tensile strength of each bolt

Yield line theory can be used to determine the capacity of a connection as well as the force
that can be exerted on a bolt. However, yield line theory does not provide bolt force
predictions that include prying action forces. Hence, Kennedy, et al. (1981) suggested a
method to predict the bolt forces as a function of the applied flange force. [12]

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The Kennedy method is based on the split-tee analogy and three stages of plate behavior.
He considered a split-tee model, Figure 2.7, consisting of a flange bolted to a rigid support
and attached to a web through which a tension load is applied.

Figure 2-7 Kennedy’s split-tee model

At the lower levels of the applied loads, the flange behavior is termed as “thick plate
behavior”, as plastic hinges have not formed in the split-tee flange, Figure 2.8a. As the
applied load is increased, two plastic hinges form at the centerline of the flange and each
web face intersection, Figure 2.8b. This yielding marks the “thick plate limit” and the
transition to the second stage of plate behavior termed as “intermediate plate behavior”.
At a greater applied load level, two additional plastic hinges form at the centerline of the
flange and each bolt, Figure 2.8c. The formation of this second set of plastic hinges marks
the “thin plate limit” and the transition to the third stage of plate behavior termed as “thin
plate behavior”.

(a) (b) (c)

First stage/ thick plate behaviour Second stage/ intermidiate plate behaviour Third stage/ thin plate behaviour

Figure 2-8 Flange behavior models

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Bruhn and Niu

Both Bruhn and Niu studied the effect of prying on tension clips from aeronautical
engineering point of view. However since tension clips used on aircraft assemblies and T-
stub connections have similar characteristics in terms of prying action, the concept applies
for both.

Bruhn presented a simple analytical approach by using static equilibrium.

Q b

F a (2-7)

Where, Q is prying force

F is the applied load

a is distance between the bolt axis and the edge

b is the distances between the bolt axis and the root radius

Whereas Niu emphasized the impossibility of having an exact calculation for prying effect
due to plenty of dependent variables like: [9]

 Geometry of the connection

 Type, material and location of the fastener
 Preload in fastener
 Distribution shape of contact forces forming the prying load
 Thickness ratio of flange and web

Kristian Ydstebo

Kristian Ydstebo, by using H. Ersland’s prying force model, calculated the prying force
by modeling the T-stub shown in Figure 2.9, where the bolt and the prying force are
modeled as roller support and the distance between bolt axis and edge of the end-plate
taken as the maximum distance provided by ES EN 3:1-8, n is 1.25m. Since the system is
statically indeterminate, the unit load method was used to determine the prying force, Q.

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Figure 2-9 Model for determining the prying force, Q

Using the unit load method, Kristian Ydstebo determined the bolt force as 0.64F and the
prying force as 0.14F meaning the prying force exerts an additional 28% of the load
applied. [8]

Figure 2-10 Prying force on a T-stub

However, this model only focused on the equilibrium condition of the system and doesn’t
consider the contribution of the thickness or the material property of the flange.

2.3. Existing Expressions for Prying Action

Different codes and standards define prying action a little differently and consider its
effects in different ways. Even though they all consider this effect in the design of
connections, some codes consider it implicitly by calculating the amount of prying force
created while others consider the effect explicitly by calculating the resistance of the
connection to take this effect in to consideration.

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Load and Resistance Factor Design, LRFD and ASD

The Load and Resistance Factor Design specification for structural steel buildings, LRFD,
defines prying action as a lever action that exists in connections in which the line of
application of the applied load is eccentric to the axis of the bolt, causing deformation of
the fitting and an amplification of the axial force in the bolt.

The LRFD specification states that the required tensile strength shall include any tension
resulting from prying action produced by deformation of the connected parts.

Even though, LFRD and ASD vary by the factor of safety they use for the calculation of
the design resistance of flanges, the concept behind prying action is the same.

Chinese code

The code of practice for the structural use of steel 2011, Hong Kong, states that

a) Design against prying force is not required provided that all the following
conditions are satisfied.
i. Bolt tension capacity Pt is reduced to
Pnom  0.8 At Pt (2-8)

In which Pnom is the nominal tension capacity of the bolt and At is the tensile
stress area of a bolt
ii. The bolt gauge G on the flange of UB, UC and T sections does not exceed
0.55B, in which B is total width of the flange, see figure 3.1

Figure 2-11 Prying Force according to the Chinese code

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b) If the conditions described in (a) above cannot be satisfied, the prying force Q
should be calculated and taken into account and Ftot should be calculated as
follows:

Ftot  Ft  Q  Pt (2-9)

Ftot is the total applied tension in the bolt including the prying force, and Ft is the
tension force in the bolt.

Even though the Chinese code recommends taking prying force in to account when
calculating the total applied tension force in bolts, it doesn’t state a way to calculate this
prying force.

Indian Standard

The Indian Standard, IS 800: 2007 defines prying force as an additional force
developed in a bolt as a result of the flexing of a connection component such as a
beam end plate or leg of angle.

IS 800:2007 states that if the prying force, Q is significant, it shall be calculated as

given below and added to the tension in the bolt.
lv  f obet 4 
Q   Te  
2le  27lelv2 
(2-10)

Where
lv = distance from the bolt centerline to the toe of the fillet weld or to half the
root radius of a rolled section
le = distance between prying force and bolt centerline and is the minimum of
either the end distance or the value given by:
f o
l e  1.1t
fy
(2-11)

Where: Β = 2 for non pre-tensioned bolt and 1 for pre-tensioned bolt,

η = 1.5,
be = effective width of flange per pair of bolts,
fo = proof stress in consistent uints, and
t = thickNess of the end plate.

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Figure 2-12 Combined prying force and tension according to the Indian standard

Ethiopian Building Code and Standard

The Ethiopian Building Code and Standard, Design of Steel Structures, ES EN 1993-1-
8:2013 implicitly takes prying effects into consideration when determining the design
tension resistance of a T-stub flange. It also states when fasteners are required to carry an
applied tensile force, they should be designed to resist the additional force due to prying
action. However, it doesn’t state how to calculate these additional forces.

Prying forces may develop if Lb ≤ Lb*

Where; Lb is the bolt elongation length, taken equal to the grip length (total
thickness of material and washers), plus half the sum of the height of the
bolt head and the height of the nut.
8.8 * m3 * As
L 
*

 leff t 3f
b
(2-12)

ES EN like Eurocode3 divides the possible failures in to three modes. Mode 1 is the
complete yielding of the flange; Mode 2 is the combination of bolt failure with yielding of
the flange while Mode 3 is bolt failure.

In cases where prying forces may develop, the design tension resistance of a T-stub flange
FT , Rd
should be taken as the smallest value for the three possible failure modes 1, 2, and

3.
Mode 1: connections with thin end-plate
In connections where thin end-plate relative to tensile bolt resistance is used,
complete yield of the plate flange is observed. Design resistance of the t-stub can
be obtained from the equation:

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4M pl ,1,Rd
FT ,Rd 
m (2-13)

where: Mpl,Rd is the yielding moment of the end-plate

m is the distance between bolt axis and weld or root of I or H profile.
Mode 2: connections with medium thickness end-plate
In connections where the thickness of the end-plate is greater than in above, a
partial plasticization of the end-plate is observed. Deformations of the end-plate
cause the increase in force in the blots and finally leading them to failure. Tensile
resistance of the connection can be obtained from the equation:
2M pl , 2, Rd  n Ft , Rd
FT , Rd 
mn (2-14)

Where: Mpl,Rd is the yielding moment of the end-plate

Ft, Rd is the design tension resistance of a bolt
m is the distance between bolt axis and weld or root of I or H
profile.
n is the distance between bolt axis and edge of the end-plate, but n
≤ 1.25m.
Mode 3: connections with thick end-plate
In connection where a thick end-plate is used, the deformation of the plate is very
small and the failure will be a bolt failure. Design resistance of the t-stub can be
obtained from the equation:
FT , Rd   Ft , Rd
(2-15)

Where: Ft, Rd is the design tension resistance of a bolt

Yielding moment of the end-plate can be 2obtained from the equation:

0.25 l eff ,1t f f y
M pl ,1, Rd 
 Mo (2-16)
0.25 l 2
t fy
M pl , 2, Rd 
eff , 2 f f

 Mo (2-17)

The fact that this standard doesn’t explicitly consider the effect of prying force on the
calculation of the design resistance of flanges is the main reason for this research.

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2.4. Equivalent T-stub

According to ES EN 3:1-8 [3], it is possible to use an equivalent T-stub in bolted

connections for modeling the design resistance of the following basic components:

 Column flange in bending

 End-plate in bending
 Flange cleat in bending
 Base plate in bending under torsion

From the four basic components stated in the standard, only end-plates in bending were
considered for this research.

The equivalent T-stub model is a geometrical idealization of the tension zone where as the
name indicates, is a T profile made of web in tension and a flange in bending. The
equivalence will be reached through the definition of an appropriate length of the
equivalent T-stubs called effective length, leff [7].

Figure 2-13 T-stub geometry

The effective length of an equivalent T-stub, a notional length which doesn’t necessarily
correspond to the physical length of the basic joint component that it represents, should be
such that the design resistance of its flange is equivalent to that of the basic joint
component that it represents [3].

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Figure 2-14 Dimensions of an equivalent T-stub flange

When determining the design resistance of a T-stub flange, one of the three different failure
modes will be the dominant failure mode. For failure mode 1 and 2, the plastic moment
must be known. The effective length is then necessary to know when calculating the plastic
moments, see Equation 2.16 and 2.17. The effective length depends on the positioning of
the bolts and whether the column flange is stiffened, unstiffened or if it is an end-plate.
The standard also divided the failure yield patterns in to circular and non-circular patterns
as well as individual bolt-rows and part of a group of bolt-rows.

The formation of non-circular yield patterns requires the development of prying forces in
the T-stub, while the formation of circular yield patterns doesn’t require the development
of prying forces [3]. Hence, this paper only considered the formation of non-circular yield
patterns and calculated the effective lengths accordingly. It should also be noted that since
the design resistance formulae in equations 2-13, 2-14, and 2-15 are only valid for a T-
stub with two bolts per row [7].

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3. MATERIALS AND METHOD OF ANALYSIS

3.1. Study Parameters

The effect of prying action on the tensile resistance of a column flange and an end-plate in
bending are studied by varying the following study parameters;
 Thickness of the flange (tf),
 Distance between bolt axis and root of the profile (m),
 Yield strength of the plate (fyp), and
 Yield strength of the bolt (fyb).

The studied T-stub is an IPE500 section cut in the middle in to two T-stubs and is bolted
together using two bolt-rows (a total of four bolts). M16 bolts were used for the simulation
process.

Taking availability of material properties in the Ethiopian market for practical

consideration, the yield strengths of the flange were taken as S235H, S275H, and S355H.
Table 3-1 Mechanical properties of flange
Yield Ultimate
Material Density Young's Poisson
Stress Stress
Type (kg/m3) Modulus(kN/mm2) Ratio
(N/mm2) (N/mm2)

S 235H 235 360 7850 210 0.3

S 275H 275 430 7850 210 0.3
S 355H 355 510 7850 210 0.3

The bolt grades were chosen arbitrarily, taking the two smallest grade and the two highest
grades stated in ES EN 1993-1-8, table 3.1.
Table 3-2 Mechanical properties of bolt
Yield Ultimate
Material Density Young's Poisson
Stress Stress
Type (kg/m3) Modulus(kN/mm2) Ratio
(N/mm2) (N/mm2)
4.6 Bolt 240 400 7850 210 0.3
5.6 Bolt 300 500 7850 210 0.3
8.8 Bolt 640 800 7850 210 0.3
10.9 Bolt 900 1000 7850 210 0.3

ES EN 3:1-8 recommends the use of the material types in Table 3.1 for steel thickness ≤
40mm. however, since plate thicknesses above 25mm are seldom used, the range of the
plate thickness used are as follows;

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Table 3-3 End plate thickness

Material Type Thickness(mm)
S 235H 5 10 15 20 25
S 275H 5 10 15 20 25
S 355H 5 10 15 20 25

The distances between the bolt axis and the root radius are chosen by calculating the
maximum distances allowed by the standard for an IPE500 section and taking that as a
mean value. According to ES EN 3:1-8, in order to avoid prying action, the distance
between the bolt axis and the edge, n, has to be less than or equal to 1.25 times the distances
between the bolt axis and the root radius, m. The calculation for the maximum distances
allowed by the standard to avoid prying action is as follows:

b  n  m  0.8r  t w  0.8r  n  m
200  n  m  0.8 * 21  10.2  0.8 * 21  n  m
200  2n  2m  43.8
200  43.8  2n  2m, n  1.25m
156.2  21.25m  2m
156.2
m max   34.71mm
4.5
n max  1.25 * m  43.39mm

Table 3-4 Values for n and m

m(mm) 15 25 34.71 45 55 65 70
n(mm) 18.75 31.25 43.39 56.25 68.75 81.25 87.5

Therefore, the values of m were taken as shown in Table 3.4 by taking the minimum as an
approximation of half of the mean and the maximum as double of the mean. For every
configuration, the values of n were calculated by taking the maximum limit of n  1.25m

Table 3-5 Values of the independent variables

m (mm) 15 25 34.71 45 55 65 70
tf (mm) 5 10 15 20 25
fyb (MPa) 240 300 640 900
fyp (MPa) 235 275 355

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3.2. Finite Element Model

Finite element model of the T-stub connections have been created using the finite element
program, Abaqus version 6.13. The true stresses and strains, calculated from the
engineering stresses and strains, were used for the constitutive models of the T-stubs and
the bolts. Figure 3-1 shows models for S 235H steel and bolt grade 5.6.

T-stub Bolt
700
600
True Stress (MPa)

500
400
300
200
100
0
0 0.05 0.1 0.15 0.2
True Plastic Strain

Figure 3-1 Constitutive model for T-stub and bolt

The models analyzed were the assemblies of subcomponents which were modeled
separately. The assembled model consists of four bolts, a supporting plate, and two T-
stubs. However, to minimize the computational time, the T-stubs were cut in to two
symmetrical parts and one was used for the simulations. The final assembled model, Figure
3.2, consists of two bolts, a supporting plate and two T-stubs.

Figure 3-2 Assembled model and simplified bolt

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3.2.1. Simplified Bolt

A simplified element model of the bolt without threads has been used. Because the threads
on the bolts have been ignored, the tensile area of the bolt was used to calculate the
diameter. For M16 bolts with a tensile area As of 157mm2, the diameter is 14.14mm. The
grip length for every configuration was taken as the sum of the thicknesses of the two T-
stubs and the washer. The grip length, therefore the length of the bolt differs for every
flange thickness used. The bolt and nut were modeled as one part; however, the washer
was modeled independently and assembled.

3.2.2. Material data

The materials are assumed to behave elastically until they reach their true yield stress and
plastically until an ultimate stress is reached. The plastic strain is taken as zero at yielding
and true plastic strain is taken as the corresponding strain to the ultimate stress. Elastic and
plastic material properties used in the finite element analysis for the bolts, flanges and
webs are as follows. For detailed calculations, see Appendix B.

Table 3-6 Material data for FEM

Elastic Properties Plastic Properties
Material Young’s Poisson’s Yield Plastic
Modulus(MPa) Ration Stress(MPa) Strain
235.26 0
S 235H 210000 0.3
435.6 0.189
275.36 0
S 275H 210000 0.3
516 0.18
355.6 0
S 355H 210000 0.3
601.8 0.163
240.27 0
Bolt class 4.6 210000 0.3
488 0.197
300.43 0
Bolt class 5.6 210000 0.3
600 0.179
641.95 0
Bolt class 8.8 210000 0.3
896 0.109
903.86 0
Bolt class 10.9 210000 0.3
1100 0.09

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3.3. Sampling Technique

The independent variables under considerations; thickness of the flange, tf, the distance
between bolt axis and root of the profile, m ,yield strength of the plate, f yp, and yield
strength of the bolt, fyb when combined result in 360 combinations. Out of these
combinations, Latin hypercube sampling method, LHS, was used to select 32
representative combinations.

Table 3-7 Statistical variation of random variables

variable unit 𝑥̅ i σi
m mm 17.101 12.873
tf mm 10 6.455
fyb MPa 288.333 61.101
fyp MPa 520 308.545
Table 3-8 Configurations used
Configurations m(mm) tf (mm) fyb (MPa) fyp (MPa)
1 35 5 300 355
2 45 15 640 235
3 35 25 900 235
4 65 10 900 355
5 65 10 240 235
6 35 15 640 355
7 55 25 240 275
8 55 20 300 235
9 55 20 640 235
10 45 10 900 355
12 45 10 300 275
13 70 25 900 275
14 70 5 640 355
15 25 15 900 235
16 45 5 300 355
17 25 15 640 355
19 35 20 240 235
20 55 25 640 275
21 55 5 640 275
22 35 20 300 355
23 65 20 640 275
24 55 10 640 275
25 25 15 240 235
26 65 10 300 275
27 45 25 640 355
28 55 15 900 355
29 45 20 240 355
30 70 15 900 355
31 35 25 300 355
32 45 15 240 235

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Out of these 32 combinations/ configurations, configuration 11 was eliminated as it

doesn’t satisfy the minimum end distance requirement stated in ES EN 3:1-8, 3.5, Table
3.3. And configuration 18 was eliminated because the configuration is the same as
configuration 2. Therefore 30 configurations were used to best represent the possible
combinations of the random variables.

3.3.1. Sensitivity Analysis

Sensitivity analysis is the analysis of the effect of input quantity variability on the
output quantity variability. It answers the question as to which quantities are dominant,
and therefore they have to be paid particular attention to when (i) preparing the input
values; (ii) considering and deciding on improvement of technological procedures; (iii)
conceiving and organizing the control activities. Also, economic criteria are usually
included into cases (ii) and (iii). Moreover, it is possible to distinguish by means of the
sensitivity analysis which quantities are in a rather low influential position; therefore
they can be considered only in a deterministic way (as non-random ones). This can
contribute to simplification and acceleration both of the calculations and modeling [13].
Although range is the simplest measure of spread for a given data, it is not considered a
very reliable measure because it is highly sensitive to the sample size and is very sensitive
to the extreme values. Hence, coefficient of variation, CoV, is used to quantify the spread
of the data points. This statistic is the ratio of the standard deviation to the mean. As such,
it provides a normalized measure of the spread. It is often expressed in the form of a
percent.

Coefficient of variation (CoV)

xi
CoVi  *100%
i (3-1)
Sensitivity factor

FT , Rd xi
i  *
i FT , Rd
(3-2)
Uncertainty Analysis

U i  CoVi * i , i = random variable index (3-3)

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The uncertainty coefficients were calculated by multiplying the coefficient of variation

and the sensitivity factor. The uncertainty analysis states the percentage contribution of
the variables. If the Ui value is positive then the variable has a positive contribution which
means increasing those particular variable results in an increased value of the dependent
variable and if it is negative it has a negative contribution which means decreasing those
particular variable results in an increased value of the dependent variable.

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4. ANALYSIS

4.1. Validation of the Finite Element Model

As experiments were not performed in this study, the use of simulation software,
ABAQUS, was necessary. The test performed by Kristian Ydstebo[8] at the University of
Stavanger, Norway where the t-stubs were tested by clamping the web of the bottom t-stub
and pulling the web of the top t-stub with a constant velocity are used to check the
reliability of the simulations done in ABAQUS.

Table 4-1 Material data for validation

Young’s Poisson’s Plastic
Material Stress(MPa)
Modulus(MPa) Ratio Strain
fy 355.6 0
S 355H 210000 0.3
fu 601.8 0.163
210000 0.3 fy 641.95 0
Bolt class 8.8
fu 896 0.109

From the experiment, it was found that the failure load was 177.4kN with 29.6mm
deflection and from the finite element model, it was found that the failure load was
191.22kN with 29.03mm deflection, measured at the center of the flange, which has a 7.7%
error. Both samples showed bolt fracture as the failure mode with their edges still in
contact. It can be observed that the finite element model result is in good agreement with
the experimental result. The similarity of failures can be seen in Figure 4-1.

Figure 4-1 Comparison of FEM and experimental result

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4.2. Analytical Study of the Finite Element Model

Step

The model had an initial increments size of 0.001. The total time was set to 1. Each
increment was limited by the minimum size of 1e10-30 and maximum size of 1. Total
allowed increments were 100000. If the analysis required either more increments or
increment size beyond the limitations, the analysis would be cancelled. The
limitations were set to prevent the analysis to run for long period of time without
significant progress.

Interaction

Two types of interactions were used. A General contact with an ‘All* with self’ surface
pair and a Surface-to-surface contact with a specified master and slave surfaces were used.
For both interactions, a contact property of tangential behavior with a friction coefficient
of 0.8 was used.

The bottom T-stub and the support plate were tied together using the ‘Tie’ constraint. And
the loading point and the top T-stub were constrained together using a ‘Kinematic
Coupling’ constraint with all the DoFs constrained.

Load

Tension load was applied by adding displacement in the Y-direction on the top web as a
boundary condition. This displacement was increased uniformly using amplitude. The
remaining degrees of freedom were set to be zero.

Mesh

Three-dimensional hexahedral elements with eight nodes at each corner, C3D8R, are used.
The element sizes differ, as part that are not prioritized for investigation, like the nut and
head of the bolt, and the support plate, have coarse meshes while those that are prioritized
have finer meshes. This was done to reduce the computational time.

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4.3. Prying Force Calculation

The prying force, Q, for the finite element models is calculated as the resulting bolt force,
B, minus the applied tension force, T. where the applied tension force is taken as the failure
load of the T-stub.

Since prying action occurs as the reaction of the pressing force that occurs because of the
pulling force created by the deformation of the flange, there has to be a contact between
the two T-stub flanges. Therefore, the prying forces are calculated for those configurations
whose flanges edges are still in contact at failure.

The total bolt force on the system is the

summation of the applied force and the
prying force, on both sides.
T  2 * Q  4 * B
Q
4 * B   T
2 (4-1)

The allowable prying force, Qall, on a single bolt can be calculated as the difference of the
tensile strength of a single bolt, Ft,Rd and the portion of the tension load applied on one
bolt, T/4.
T
Qall  Ft , Rd 
4 (4-2)

Hence, the additional force the bolts are subjected to is the difference between the
allowable and the applied prying forces. This allowable force is the reserve capacity the
bolts have in case of a prying action and if the existing prying force is less than this value,
the bolts can carry the additional loads. However, if the prying force is greater than the
allowable, then the bolts will have to carry additional loads.

Bo  Q  Qall (4-3)

This is the case for all configurations except those with no prying force generated, whose
tension capacity can’t carry the applied tension load and doesn’t have an allowable prying
force.

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4.4. Design Resistance According to ES EN 1993-1-8:2013

The design tension resistance of the different T-stub configurations based on the
calculations given in ES EN 3:1-8 has been calculated. In order to achieve the best basis
for comparing the load capacity calculations with the results obtained from the finite
element analysis, the partial safety factors are set equal to 1.0. Since the factor is used as
a safety for failure, the capacity is meant to have a lower value than the actual capacity;
the best assessment of the regulations is without the partial safety factor.

Effective length, leff

According to ES EN 3:1-8, the effective length shall be determined using one of the three
tables given in the standard; effective length for an unstiffened column flange, effective
length for a stiffened column flange and effective length for an end-plate [3]. Out of the
different bolt-row locations, the one used for this computation is the end bolt-row location.

Table 4-2 Effective length calculations

Bolt-row Bolt-row considered as
Location part of a group of bolt-rows
end
End-plate 2m + 0.625e + 0.5p
bolt-row
Mode 1 ∑leff,1 = ∑leff,nc
Mode 2 ∑leff,2 = ∑leff,nc

Since the effective length of a T-stub is a function of edge distance, distance between bolts
and the distance between the bolt axis and the root radius, for every configuration the
effective length varies. For every configuration, the effective length is calculated by
considering the bolt rows as a part of a group.

Since the formation of circular yield patterns doesn’t require the development of prying
forces but the formation of non-circular yield patterns does, the effective length is also
calculated for the non-circular yield pattern cases only. As the mode of failure is the same
whether the bolt-rows are considered individually or as part of a group, only one is
considered; the bolt-rows are considered as a part of a group.

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5. RESULTS AND DISCUSSION

The results obtained from the finite element models are discussed in terms of the tension
capacities and the prying forces generated. Also, by using sensitivity/ uncertainty analysis,
the percentage contribution of the different variables; m, tf, fyb, and fyp were obtained. This
process is done for both the results obtained from the formula provided by ES 3:1-8 for
the calculation of tension resistance of T-stubs and from the results obtained from the finite
element models.

5.1. Evaluation of the Finite Element Models

From the 30 configurations, the detailed discussions of three representative configurations
are presented as follows:

Configuration 4

Mode 1 Mode 2 Mode 3 T-Stub B(KN)

800
700
600
Load (kN)

500
400
300
200
100
0
0 10 20 30 40 50 60 70 80 90 100

∆ (mm)

Figure 5-1 Load-deflection curve of configuration 4

The load-deflection curves of the T-stub and the bolt show elastic-plastic behavior until
ultimate failure. The governing failure mode for configuration 4 is mode 1 indicating the
yielding of the flange at an applied failure load of 136.9kN. It can be seen from the curve
that the T-stub flange yields at a load of 129.6kN which is only slightly lower than the load
predicted by the analytical formula in the code. However, the failure load of the T-stub is
279.7kN which means mode 1 shows a large reserve capacity beyond the failure criterion
of the code.

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Figure 5-2 T-stub stress at 129.6kN

The T-stub flange yielded first at the root of the profile at an applied load of 129.6kN with
a deflection of 2.4mm but the ultimate tensile capacity of the system is 279.7kN with a
deflection of 80.74mm.

Figure 5-3 Bolt and T-stub stresses at 279.9kN

The curve also shows the tension forces in the bolts are much higher than the applied force
because of the presence of prying action in the T-stub. The ultimate failure of the T-stub
occurs when the forces on the bolts reach 690.8kN which is more than the applied tension
load, 279.7kN. This indicates prying force, 205.55kN, is generated on each edge and there
are additional forces, 31.4.kN, induced on the bolts due to this action. This can be seen in
figure 5.4 where the bolt force versus applied force is plotted to show how much the forces
on the bolts deviated from the forces they should have had if there was no prying action.

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800
700

Bolt Force (kN)

600
500 Q(kN)
400
300
200
100
0
0 50 100 150 200 250 300
Applied Force (kN)

Figure 5-4 Bolt Vs. Applied force for configuration 4

Configuration 8

Mode 1 Mode 2 Mode 3 T-Stub B(KN)

450
400
350
300
Load (kN)

250
200
150
100
50
0
0 5 10 15 20
∆ (mm)

Figure 5-5 Load-deflection curve of configuration 8

The code predicts the failure of the configuration 8 by yielding of the flange with bolt
failure at an applied force of 241.825kN after removing the safety factors in the
calculations. The finite element model shows the T-stub fails by bolt failure at an applied
load of 280.8kN. Here, it can be seen that mode 3, 282.6kN, predicts the failure more than
mode 2, 241.825kN, this is because since the yield strength of the bolt is small, the bolt
yields at an applied load of 131.098kN before the flange yielded. The flange yielded but
never reached the ultimate stress because the bolt fractured.

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Figure 5-6 T-stub stress at 131.098kN

Figure 5-7 Bolt and T-stub stresses at 280.8kN

It can be seen that the tension forces in the bolts are much higher than the applied force
because of the presence of prying action in the T-stub. The ultimate failure of the T-stub
occurs when the forces on the bolts reach 377.4kN which is more than 280.8kN, the
ultimate axial capacity. This indicates prying force, 48.6kN, is generated on each edge and
there are additional forces, 23.8kN, induced on the bolts due to this action. This can be
seen in figure 5.8 where the bolt force versus applied force is plotted to show how much
the forces on the bolts deviated from the forces they should have had if there was no prying
action, although the decrease of loads after yield cannot be explained. Configuration 8 has
the smallest prying force than the rest of the configurations. This is because the T-stun
flange is thick, 20mm, and the yield strength of the bolt is small, 300MPa.

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400
350
Q (kN)

Bolt Force (kN)

300
250
200
150
100
50
0
0 50 100 150 200 250 300
Applied Force (kN)

Figure 5-8 Bolt Vs. Applied force for configuration 8

Configuration 13

Mode 1 Mode 2 Mode 3 T-Stub B(KN)

800

700

600
Load (kN)

500

400

300

200

100

0
0 5 10 15 20
∆ (mm)

Figure 5-9 Load-deflection curve of configuration 13

The governing failure mode for configuration 13 is mode 2 indicating a bolt failure with
yielding of the flange at an applied failure load of 458.9kN and it can be seen from the
curve that the T-stub failed at a load of 460.614kN which is only slightly higher than the
load predicted by the analytical formula in the code.

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Both the flange and the bolts yielded at the same time at an applied load of 424.5kN and
the system fails at an applied load of 460.614kN. This shows there is no reserve capacity
in the failure mode which is not a desirable condition.

Figure 5-10 T-stub stress at 424.5kN

Figure 5-11 Bolt and T-stub stresses at 460.614kN

700
600
Q (kN)
Bolt Force (kN)

500
400
300
200
100
0
0 100 200 300 400 500
Applied Force (kN)

Figure 5-12 Bolt Vs. Applied force for configuration 13

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The curve shows the tension forces in the bolts are much higher than the applied force
because of the presence of prying action in the T-stub. The ultimate failure of the T-stub
occurs when the forces on the bolts reach 650.325kN which is more than 460.614kN, the
applied tension load. This indicates prying force, 94.867kN, is generated on each edge and
there are additional forces, 21.3kN, induced on the bolts due to this action. This can be
seen in Figure 5.12 where the bolt force versus applied force is plotted to show how much
the forces on the bolts deviated from the forces they should have had if there was no prying
action.

The summary output of the finite element models for the 30 combinations is shown in
Table 5-4.

Table 5-1 Prying force calculation

Configuration B (kN) T (kN) Q (kN) Qall (kN) Bo (kN) Failure Mode
1 376.8 145.18 115.81 34.35 23.55 Both
2 562.68 334.704 113.99 29.36 27.63 Bolt Failure
3 690.8 565.004 62.89 0.05 31.4 Flange Yielding
4 690.8 283.60 203.59 71.37 31.4 Flange Yielding
5 306.46 144.19 81.13 20.47 20.09 Bolt Failure
6 562.68 393.90 84.39 14.56 27.63 Bolt Failure
7 302.51 245.29 0 0 0 Bolt Failure
8 377.93 280.75 48.58 0.45 23.83 Bolt Failure
9 562.688 362.22 100.23 22.48 27.63 Both
10 690.8 319.56 185.62 61.41 31.4 Flange Yielding
12 376.8 204.09 86.35 19.63 23.55 Bolt Failure
13 650.32 460.61 94.85 26.15 21.28 Both
14 562.68 185.03 188.83 66.78 27.63 Flange Yielding
15 690.8 438.61 126.09 31.65 31.4 Flange Yielding
16 376.8 134.94 120.93 36.92 23.55 Bolt Failure
17 562.68 442.94 59.87 2.31 27.63 Bolt Failure
19 306.46 245.06 0 0 0 Bolt Failure
20 562.68 454.37 54.16 0 27.63 Bolt Failure
21 562.68 207.96 177.36 61.05 27.63 Flange Yielding
22 376.8 306.97 0 0 0 Bolt Failure
23 562.16 362.47 99.85 22.42 27.50 Both
24 562.68 242.84 159.92 52.33 27.63 Flange Yielding
25 306.46 245.65 0 0 0 Bolt Failure
26 376.8 175.54 100.63 26.76 23.55 Bolt Failure
27 562.688 487.31 0 0 0 Bolt Failure
28 690.8 413.49 138.65 37.93 31.4 Flange Yielding
29 306.46 245.21 0 0 0 Bolt Failure
30 690.8 382.83 153.98 45.59 31.4 Both
31 373.86 307.59 0 0 0 Bolt Failure
32 306.46 201.44 52.51 6.159 20.09 Bolt Failure

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According to ES 3:1-8, prying forces may develop if Lb ≤ Lb*. By calculating the

equivalent Lb and Lb* values for all configurations, it was found that configurations 3, 19,
22, 27 & 31 have not developed prying forces while the remaining 25 configurations have.
Prying forces only develop when the ends of the flanges are in contact due to the applied
load. Taking this in to consideration, configurations 19, 22, 27 & 31 indeed haven’t
developed prying forces. However that is not the case for configuration 3, which developed
a prying force of 62.898kN. In this configuration, the contribution of the yield strength of
the bolt can be observed. Even though the thickness of the flange is large, which have a
negative contribution to the prying force, since the yield strength of the bolt is large; prying
force was developed at the edges. Figure 5-4(a) shows how the edges of the flanges in
configuration 3 are still in contact at failure and (b) shows those of configuration 19 are
not.

(a) (b)

Figure 5-13 Contact criteria for prying action

From table 5-1, it can be seen that there is an average 30% increase in bolt force due to the
presence of prying force. It can also be seen that all configurations with low yield strength
bolts, except configuration 1, failed by bolt failure, mode 3. Configuration1 had a mode 2
failure because the thickness of the flange is thin.

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Sensitivity Analysis – Tension Capacity

Using Equations 3-1, 3-2 and 3-3, the sensitivity factors and uncertainty are obtained.
From this it can be seen that the thickness of the T-stub flange and the yield strength of
bolts govern the tension resistance of the T-stub more than m and fyp.

Table 5-2 Sensitivity Analysis parameters for FEM

αi CoVi Ui %
m -0.32378 29% -0.09283 -14%
tf 0.529325 43% 0.22505 35%
fyb 0.560595 48% 0.26856 42%
fyp 0.310197 18% 0.055476 9%

fyp

fyb

tf

-20% -10% 0% 10% 20% 30% 40% 50%

Figure 5-14 Sensitivity analysis for the finite element model

Sensitivity Analysis – Prying Force

Using Equations 3-1, 3-2 and 3-3, the sensitivity factors and uncertainty are obtained.
From this it can be seen that tf and fyb govern the prying force created at the edges of the
T-stub more than m and fyp.

Table 5-3 Sensitivity Analysis parameters for prying action

αi CoVi Ui %
m 0.484768 29% 0.182854 16%
tf -0.90923 43% -0.50963 -43%
fyb 0.681353 48% 0.437812 37%
fyp 0.661165 18% -0.0428 -4%

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fyp

fyb

tf

-50% -40% -30% -20% -10% 0% 10% 20% 30% 40% 50%

Figure 5-15 Sensitivity Analysis for prying force

From the sensitivity analysis, it can be seen that the thickness of the flange has a negative
contribution which means increasing the thickness will significantly decrease the prying
force created, while the yield strength of the bolt has a positive contribution.

The distance between the bolt axis and the root and the yield strength of the flange also
has positive and negative contributions, respectively, even though their contributions are
not as much as the formers. This can be seen in configurations 1 and 16. For these
configurations, the role of m comes to play. These two configurations are the same except
for the values of m. now, since m has a 16% contribution to the magnitude of the prying
force, the one with the higher value of m has the larger Q, 120.93kN. But since m has a -
14% contribution to the tensile capacity, the one with the smaller m has the larger T,
145.18kN.

5.2. Evaluation of the Design Tension Resistance in ES EN 1993-1-8:2013

Using Equations 3-1, 3-2 and 3-3, the sensitivity factors and uncertainty are obtained.
From this it can be seen that the thickness of the T-stub flange and the yield strength of
bolts govern the tension resistance of the T-stub more than m and fyp.

Table 5-4 Sensitivity Analysis parameters for ES EN 3:1-8

αi CoVi Ui %
m -0.19066 29% -0.05466 -7%
tf 1.068731 43% 0.454387 60%
fyb 0.42373 48% 0.202993 27%
fyp 0.24206 18% 0.043291 6%

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fyp

fyb

tf

-20% -10% 0% 10% 20% 30% 40% 50% 60% 70%

Figure 5-16 Sensitivity analysis for ES EN 3:1-8

Even though the positive and negative contributions of the variables are the same for both
cases; the tensile resistances from the finite element models and code, there seems to be a
contradiction between which variable contribute more to the tension resistance. According
to the finite element models, the yield strength of the bolt contributes 42% while the
thickness of the flange contributes 35% but according to the analytical formula given in
the code, the yield strength of the bolt contributes 27% while the thickness of the flange
contributes 60%. This is because aside from mode 3, the formula provided in the code for
both modes 1 and 2 are predominantly influenced by the thickness of the T-stub flange.

However, since the presence of prying action induces additional loads on the bolts, there
is a chance of more bolt failures, mode 3, than modes 1 and 2. Therefore the tensile
resistance of the T-stub can also be influenced by the tension resistance of the bolts hence
the yield strength of the bolts.

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6. CONCLUSION AND RECOMMENDATIONS

6.1. Conclusion

Where there is deformation/deflection, no matter how small, there is bound to be a prying

force created. The question is whether or not the connection fails because of it. And this is
based on the capacity of the bolts to carry the additional force and the capacity of the flange
to not form a mechanism and fail. The aim of this thesis was to study the effect of prying
action on the tension resistance of beam-to-column connections and the scope of was
restricted to end plate connections for which the collapse was governed by the tension zone
idealized by T-stubs. After examining the finite element models, the following conclusions
are drawn:

 The thickness of the flange and the yield strength of the bolts contribute to the
development of larger prying forces than the yield strength of the flange and the
distance between the bolt axis and the root do.
 For thin flanges (5 and 10mm), even though the deformations are higher, the tensile
capacities are lower. But this is the case for those whose bolts have lower yield
strengths. For thin flanges, as the yield strength of the bolts increase, the tensile
capacity and the prying force generated also increase.
 For thick flanges (15, 20 and 25mm), with lower deformations, the tensile
capacities are higher. Again for thicker flanges, as the yield strength of the bolts
increase, the tensile capacity and the prying force generated also increase.
 For thin flanges, using low yield strength bolts results in lower prying force
generation with bolt fracture as the failure mode than using high yield strength
bolts with flange yielding as the failure mode.
 For thick flanges, using high yield strength bolts results in higher prying force
generation than those with lower yield strength bolts whose prying forces are
minimums, even zero.
 The best and optional combination to yield a minimum, even nonexistent, prying
force and minimum deformation is thick flanges with low yield strength bolts.
 The finite element models revealed reserve capacities in terms of ductility and
ultimate capacity for ductile failure mode 1.

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6.2. Recommendation

The following recommendations are given for future works:

 An equation for the calculation of prying force should be given in the code.
 The requirement for the development of prying should be revised.
 In the finite element models, bolt preloading should be investigated to see its effect
on the tension resistance of connections.
 The effect of change of bolt position as well as the effect of bolt spacing should be
investigated.
 Since prying action bends bolts, increasing the stress on one side than the other,
this should also be investigated as to how much it affects the capacity of the bolts.

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References

[1] A. H. Salem, E. Y. Sayed-Ahmed, A. A. El-Serwi, R. A. Samaan, (2011) “Behavior

and Design of Steel I-Beam-To- Column Flushed Rigid Bolted Connections”, The
American University, Cairo, Egypt

[2] Code of Practice for the structural use of steel, 2011, Hong Kong, China

[3] Eurocode 3: Design of steel structures. Part 1-8: Design of joints, 1993-1-8:2003

[4] G. L. Kulak, J. W. Fisher and J. H. Struik, “Guide to Design Criteria for Bolted and
Riveted Joints”, 2nd edition, American Institute of Steel Construction

[5] Indian Standard: General Construction in Steel – Code of Practice (Third Revision), IS
800: 2007

[6] I. O. Adegoke, “Ductility of Thin Extended Endplate Connections”, University of the

Witwatersrand, Johannesburg, South Africa

[7] J. Jaspart and K. Weynand, “Design of joints in steel and composite structures”, ECCS-
European Convention for Constructional Steelwork

[8] K. Ydstebo (2017) “Capacity of Bolted T-stub Connections between Different

Materials Subjected to Tension and Thermal Load”, University of Stavanger

[9] M. Atasoy (2012), “Determination of Prying Load on Bolted Connections”, Middle

East Technical University

[10] P. Zoetemeijer (1974), “A Design Method for the Tension Side of Statically Loaded,
Bolted Beam-To-Column Connections”, Stevin Laboratory, the Netherlands

[11] R. S. Nair, P. C .Birkemoe and W. H. Munse, (1969), “Behavior of Bolts in

Tee-Connections subject to Prying Action”, University of Illinois, U.S.A

[12] Thimmapuram, Vinod-Kumar (2011), “Finite Element Modeling and Study of Angle
Connections”, B. Tech JNTU, Hyderabad, India

[13] Z. kala, J. kala, “sensitivity analysis of lateral buckling stability problems of hot-rolled
steel beams”, Slovak Journal of Civil Engineering.

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APPENDICES

Appendix A
Result output values using Latin hypercube sampling method

Result Output Values Corrected Values

Con. m(mm) tf(mm) fyb(MPa) fyp(MPa) m(mm) tf(mm) fyb(MPa) fyp(MPa)
1 32.13 5.28 296.45 339.08 35 5 300 355
2 44.15 16.56 713.18 237.59 45 15 640 235
3 39.85 26.21 812.12 230.48 35 25 900 235
4 63.67 8.43 899.47 300.38 65 10 900 355
5 68.55 9.27 227.88 222.50 65 10 240 235
6 39.38 15.93 507.91 326.59 35 15 640 355
7 55.19 22.48 187.54 295.53 55 25 240 275
8 51.63 19.95 459.19 213.19 55 20 300 235
9 55.05 20.73 580.81 250.08 55 20 640 235
10 41.83 11.48 1184.57 332.60 45 10 900 355
11 0.04 3.79 263.75 266.33 15 5 240 275
12 40.20 10.05 434.32 281.14 45 10 300 275
13 78.64 24.72 1037.10 285.94 70 25 900 275
14 73.34 1.75 483.66 419.94 70 5 640 355
15 25.11 14.07 852.46 156.73 25 15 900 235
16 46.66 6.48 355.42 310.34 45 5 300 355
17 19.01 14.69 605.68 354.17 25 15 640 355
18 43.30 15.31 532.09 244.06 45 15 640 235
19 37.20 18.52 82.55 185.93 35 20 240 235
20 53.38 32.03 743.55 261.14 55 25 640 275
21 59.11 -2.03 631.12 305.30 55 5 640 275
22 34.82 19.22 326.82 315.53 35 20 300 355
23 61.29 17.85 556.34 271.37 65 20 640 275
24 58.29 10.78 657.33 290.73 55 10 640 275
25 29.48 12.15 2.90 201.70 25 15 240 235
26 66.36 7.52 408.88 276.29 65 10 300 275
27 46.85 23.52 684.58 346.18 45 25 640 355
28 57.09 17.20 776.25 363.48 55 15 900 355
29 43.44 21.57 140.53 374.96 45 20 240 355
30 88.44 12.80 957.45 390.73 70 15 900 355
31 31.40 28.25 382.67 320.93 35 25 300 355
32 49.94 13.44 144.57 255.74 45 15 240 235

Configurations 2 and 18 have the same combinations, hence, one needed to be removed to
avoid redundancy. Configuration 11 had to be removed because it does not satisfy the edge
distance requirement given in EC3:1-8.

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Appendix B
Material Data

Calculations of the material data of a bolt, bolt class5.6

Yield strength, fyb = 300MPa

Ultimate tensile strength, fub = 500MPa

Young’s Modulus, E = 210GPa

Elongation after fracture, δ = 20%

Engineering elastic strain:

fy 300MPa 300
 eng ,el     0.001429
E 210GPa 210000

True elastic strain:

 true ,el  ln 1   eng ,el    eng ,el  ln 1  0.001429   0.001429  0

Engineering plastic strain:

 eng , pl     eng ,el  0.2  0.001429  0.1986  0.2

True yield stress:

 true  f y 1   eng ,el   300 MPa 1  0.001429   300 .43 MPa

True ultimate stress, plastic:

 true , pl  f u 1   eng , pl   500 MPa 1  0.2   600 MPa

True plastic strain:

 true
 true , pl  ln 1   eng , pl    ln 1  0.2 
300.43MPa
 0.179
E 210GPa

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Appendix C
Design Tension Resistance of a T-stub flange According to ES EN 1993-1-8:2013

Given:

Yield strength of the bolt, fyb = 240MPa

Ultimate tensile strength of the bolt, fub = 400MPa

Yield strength of the flange plate, fyp = 235MPa

Bolt diameter, M16

Distance between the bolt axis and the root radius, m = 30mm

Distance between the bolt axis and the edge, n = 37.5mm

Thickness of flange, tf = 10mm

Effective Length calculations

2m  0.625 e  0.5 p  2 * 30  0.625 * 37 .5  0.5 *140  153 .4375 mm

Design resistance calculation

0.25 l eff t 2f f y 0.25 *153.4375mm * 10mm  * 235 N
2

M pl ,1, Rd   mm  901445.3125N  mm
 Mo 1

Failure Mode – 1:
4M pl ,1, Rd 4 * 901445.3125N  mm
FT , Rd    120192.7083N
m 30mm

Failure Mode – 2:
2M pl , 2, Rd  n Ft , Rd 2 * 901445.3125N  mm  37.5mm * 180864N
FT , Rd    127189.4907 N
mn 30mm  37.5mm

Failure Mode – 3:
FT , Rd   Ft , Rd  180864 N
 FT ,1, Rd  120192.7083 
   
FT , Rd  Min FT , 2, Rd   Min127189.4907 N   120192.7083N  120.193KN
F  180864N 
 T ,3, Rd   

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Appendix D
Load-Deflection and Bolt vs. Applied force charts for all configurations

Configuration 1

400 400

350 350

Bolt Force (KN)

300 300
250 250
Load (KN)

200 200
150
150
100
100
50
50
0
0 10 20 30 40 50 0
0 50 100 150
∆ (mm) Applied Force (KN)
Mode 1 Mode 2 Mode 3 T-Stub B(KN)

Configuration 2
600
600

500 500
Bolt Force (KN)
Load (KN)

400
400
300
300
200
200
100

0 100
0 5 10 15 20 25 30

∆ (mm) 0
0 100 200 300 400
Mode 1 Mode 3 T-Stub B(KN) Mode 2
Applied Force (KN)

Configuration 3

800 800

700 700
Bolt Force (KN)

600 600
Load (KN)

500 500

400 400

300 300

200 200
100 100
0 0
0 2 4 6 8 10 12 14 16 18 0 100 200 300 400 500 600

∆ (mm) Applied Force (KN)

FEM No Pr. B(KN) Mode 3

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Configuration 4

800
800
700
700
600

Bolt Force (KN)

600
Load (KN)

500
500
400
400
300
300
200
200
100
100
0
0
0 10 20 30 40 50 60 70 80 90 100
0 50 100 150 200 250 300
∆ (mm)
Mode 1 Mode 2 Mode 3 T-Stub B(KN)
Applied Force (KN)

Configuration 5
350 350
300
300

Bolt Force (KN)

250
250
Load (KN)

200
200
150
150
100
100
50
50
0
0
0 10 20 30 40 50 60 70 80
0 50 100 150 200
∆ (mm)
T-Stub Mode 3 B(KN) Mode 1 Mode 2 Applied Force (KN)

Configuration 6

600 600

500 500
Bolt Force(KN)
Load (KN)

400 400

300
300
200
200
100
100
0
0 2 4 6 8 10 12 14 16 18 0
∆ (mm) 0 100 200 300 400 500
T-Stub Mode 3 B(KN) Mode 1 Mode 2 Applied Force(KN)

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Configuration 7
800 350
700
300
600

Bolt Force(KN)
250
Load (KN)

500
200
400

300 150

200 100

100
50
0
0 5 10 15 20 0
∆ (mm) 0 50 100 150 200 250 300
Mode 1 Mode 2 Mode 3 T-Stub B(KN) Applied Force(KN)

Configuration 8

450 400

400 350
350 Bolt Force (KN)
300
300
Load (KN)

250
250
200
200
150 150

100 100
50 50
0
0 5 10 15 20 0
∆ (mm) 0 50 100 150 200 250 300
Mode 1 Mode 2 Mode 3 T-Stub B(KN) Applied Force (KN)

Configuration 9

600 600

500 500
Bolt Force(KN)

400
Load (KN)

400

300
300

200
200
100
100
0
0 5 10 15 20 0
∆ (mm) 0 100 200 300 400
Mode 1 Mode 2 Mode 3 T-Stub B(KN) Applied Force(KN)

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Configuration 10

800 800
700 700
600

Bolt Force(KN)
600
Load (KN)

500
500
400
300 400

200 300
100 200
0
100
0 10 20 30 40 50
0
∆ (mm) 0 100 200 300 400
Mode 1 Mode 2 Mode 3 T-Stub B(KN)
Applied Force(KN)

Configuration 12

400 400

350 350

Bolt Force(KN)
300 300
Load (KN)

250 250
200 200
150 150
100
100
50
50
0
0
0 10 20 30 40
0 50 100 150 200 250
∆ (mm)
Mode 1 Mode 2 Mode 3 T-Stub B(KN) Applied Force(KN)

Configuration 13
700
800

700 600
Bolt Force (KN)

600 500
Load (KN)

500
400
400

300 300

200 200
100
100
0
0 5 10 15 20 0
∆ (mm) 0 100 200 300 400 500
Mode 1 Mode 2 Mode 3 T-Stub B(KN) Applied Force (KN)

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Configuration 14
600 600

500 500

Bolt Force(KN)
400 400
Load (KN)

300 300

200
200
100
100
0
0 0 50 100 150 200
0 50 100 150 200
∆ (mm) Applied Force(KN)
Mode 1 Mode 2 Mode 3 T-Stub B(KN)

Configuration 15

800 800

700 700

Bolt Force(KN)
600 600

500
Load (KN)

500
400
400
300
300
200
200
100
100
0
0 0 100 200 300 400 500
0 5 10 15 20
∆ (mm) Applied Force(KN)
Mode 1 Mode 2 Mode 3 T-Stub B(KN)

Configuration 16

400
400
350 350
Bolt Force(KN)

300 300
Load (KN)

250 250

200 200
150 150
100 100
50
50
0
0
0 20 40 60 80 100
∆ (mm) 0 50 100 150

Mode 1 Mode 2 Mode 3 T-Stub B(KN) Applied Force(KN)

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Configuration 17

600 600

500 500

Bolt Force(KN)
400 400
Load (KN)

300 300

200 200

100
100

0
0
0 2 4 6 8 10 12 14 16
∆ (mm) 0 100 200 300 400 500
Mode 1 Mode 2 Mode 3 T-Stub B(KN) Applied Force(KN)

Configuration 19

350 350

300 300
Bolt Force(KN)
250 250
Load (KN)

200 200
150 150
100
100
50
50
0
0 5 10 15 0
∆ (mm) 0 50 100 150 200 250 300

Mode 3 No Pr. T-Stub B(KN) Applied Force(KN)

Configuration 20

800 600

500
Bolt Force(KN)

600
Load (KN)

400

400 300

200 200

100
0
0 5 10 15 20 0
∆ (mm) 0 100 200 300 400 500
Mode 1 Mode 2 Mode 3 T-Stub B(KN) Applied Force(KN)

Configuration 21
600 600

500 500
Bolt Force(KN)

400
Load (KN)

400
300
300
200
200
100
100
0
0 20 40 60 80 100 0
∆ (mm) 0 50 100 150 200 250
Mode 1 Mode 2 Mode 3 T-Stub B(KN) Applied Force(KN)

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Configuration 22
450
400
400
350
350

Bolt Force(KN)
300
300
Load (KN)

250
250
200 200

150 150

100 100
50 50
0 0
0 2 4 6 8 10 12 0 50 100 150 200 250 300 350
∆ (mm)
No Pr. Mode 3 T-Stub B(KN) Applied Force(KN)

Configuration 23
600
600

500 500

Bolt Load (KN)

Load (KN)

400 400

300 300

200
200
100
100
0
0 5 10 15 20 25
0
∆ (mm) 0 100 200 300 400
Mode 1 Mode 2 Mode 3 T-Stub B(KN) Applied Load (KN)

Configuration 24
600 600

500 500
Bolt Load (KN)
Load (KN)

400 400

300 300
200
200
100
100
0
0 10 20 30 40 50 60 70 80 0
0 50 100 150 200 250
∆ (mm)
Mode 1 Mode 2 Mode 3 T-Stub B(KN) Applied Load (KN)

Configuration 25
350
350
300
300
Bolt Load (KN)

250
Load (KN)

250
200
200
150
150
100
100
50
50
0
0
0 5 10 15 20
∆ (mm) 0 50 100 150 200 250
Mode 1 Mode 2 Mode 3 T-Stub B(KN)
Applied Load (KN)

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 Addis Ababa University Addis Ababa Institute of Technology

Configuration 26
400 400
350
350
300
300

Bolt Load (KN)

Load (KN)

250
250
200
200
150
150
100
100
50
50
0
0 10 20 30 40 50 60 70 80 0
0 20 40 60 80 100 120 140 160 180
∆ (mm)
Mode 1 Mode 2 Mode 3 T-Stub B(KN) Applied Load (KN)

Configuration 27

600 600

500 Bolt Force (KN) 500

400
Load (KN)

400

300 300

200
200
100
100
0
0 2 4 6 8 10 12 14 0
0 100 200 300 400 500
∆ (mm)
No Pr. Mode 3 T-Stub P(KN) B(KN)
Applied Load (KN)

Configuration 28

800 800

700 700
Bolt Force (KN)

600 600
Load (KN)

500 500

400 400

300 300
200 200
100 100
0
0
0 5 10 15 20 25
0 100 200 300 400 500
∆ (mm)
Mode 1 Mode 2 Mode 3 T-Stub P(KN) B(KN) Applied Load (KN)

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 Addis Ababa University Addis Ababa Institute of Technology

Configuration 29
700 350

600 300

Bolt Force (KN)

500 250
Load (KN)

400 200

300 150

200
100

100
50
0
0
0 2 4 6 8 10 12 14 16
0 50 100 150 200 250
∆ (mm)
Mode 1 Mode 2 Mode 3 T-Stub B(KN) Applied Force(KN)

Configuration 30
800
800
700
700
600
Bolt Force (KN) 600
Load (KN)

500
500
400
400
300
300
200 200
100 100
0 0
0 10 20 30 40 50 0 100 200 300 400
∆ (mm)
Mode 1 Mode 2 Mode 3 T-Stub B(KN) Applied Load (KN)

Configuration 31
600 400
550
500 350
Bolt Force (KN)

450 300
Load (KN)

400
350 250
300
200
250
200 150
150
100
100
50 50
0
0 5 10 15 20 25 0
∆ (mm) 0 50 100 150 200 250 300 350
No Pr. Mode 3 T-Stub B(KN) Applied Force (KN)

Configuration 32
350
350
300
300
Bolt Force (KN)

250
250
Load (KN)

200 200
150 150
100 100

50 50

0 0
0 5 10 15 20 25 0 50 100 150 200 250
∆ (mm) Applied Load (KN)
Mode 1 Mode 2 Mode 3 T-Stub B(KN)

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