Fundamentals of Structural Design

Part of Steel Structures

Civil Engineering for Bachelors

133FSTD

Teacher: Zdeněk Sokol

Office number: B619
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Syllabus of lectures
1. Introduction, history of steel structures, the applications and some
representative structures, production of steel
2. Steel products, material properties and testing, steel grades
3. Manufacturing of steel structures, welding, mechanical fasteners
4. Safety of structures, limit state design, codes and specifications for the
design
5. Tension, compression, buckling
6. Classification of cross sections, bending, shear, serviceability limit states
7. Buckling of webs, lateral-torsional stability, torsion, combination of
internal forces
8. Fatigue
9. Design of bolted and welded connections
10. Steel-concrete composite structures
11. Fire and corrosion resistance, protection of steel structures, life cycle
assessment

1
Scope of the lecture
Basic principles of the composite structures
Shear connectors
Composite beams
Composite columns
Steel-concrete slabs

Principle of behaviour of composite beams

Steel beam and concrete slab are not connected
 They share the load (each take a part from the total)
 The deformation of both is the same – equal to δ1

slip slip

δ1

Steel concrete composite beam

 The beam and the concrete slab are connected by shear connectors eliminating
the slip on steel-concrete interface
 The composite beam takes the whole load
 The deformation is equal to δ2 < δ1

shear
shear
δ2
4

2
Steel concrete composite structures
Advantages
 Convenient stresses
(concrete in compression / steel in tension)
 Saving expensive material (steel) - low cost of the structure
 Increase of stiffness
 Better fire resistance (compared to steel structures) – no need for additional fire
protection – low cost of the structure

Steel concrete composite elements

 Beams
 Columns
 Composite slabs Shear stud

Steel concrete beam section

with welded stud
providing shear connection 5

Beam with welded shear studs

3
Standards for design of composite structures
European standard EN 1994-1-1

Design strength
 concrete ………
f cd  0,85 f ck  c
 c  1,5 

Steel
f yd  f y  M 0
 steel ………..…. 
a
 M 0  1,0

f sd  f sk  s c Concrete
 reinforcement …
 s  1,15 a, c 
Stress-strain diagram of steel and concrete
Note: for equal strain εa,c, steel gets
much higher stress than concrete
 shear connectors  V  1,25 because of different modules of elasticity

Scope of the lecture

Basic principles of the composite structures
Shear connectors
Composite beams
Composite columns
Steel-concrete slabs

4
Welded studs
 Common, cheap, simple to install
 Convenient F –  relationship
(high resistance and ductility)

Need of strong electric source for welding

Studs welded to the steel beam Shear stud

9

Welding of shear studs

Semi-automatic welding of the shear studs

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5
Advantages of studs
Deformation of ductile studs
High deformation capacity of studs allows for plastic distribution of shear forces
among the studs
As the studs at the ends of the beam are overloaded, they deform and cracks in the
concrete appear, which leads to small slip of the concrete slab, this causes the other
studs are loaded by increasing forces

Cracks in concrete
Slip

11

Resistance of studs
Characteristic resistance of the stud
 Steel failure
d2
PRk  0,8 f u
4

 Concrete failure
PRk  0,29  d 2 f ck Ecm

fu ultimate strength of material of studs, max. 500 MPa

Reduction due to stud height

 Short stud
h h 
3 4   0,2   1
d  d 
 Long stud
h   1,0
4
d 12

6
Perforated strips
Various types exist worldwide
The resistance can be increased by reinforcement placed into the holes
Non-ductile shear connection
Two types are used in Czech Republic:
 height 50 mm, thickness 10 mm, holes d = 32 mm
 height 100 mm, thickness 12 mm, holes d = 60 mm

13

Thin walled connectors

Manufactured by Hilti
Zinc-coated steel sheet, thickness 2 mm
Easy to apply, no need for electricity for welding
Connected to steel beams by two shot nails
Range of Hilti HVB connectors
Height from 80 up to 140 mm

Expensive  refurbishment

Hilti HVB shear connectors

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7
Thin walled connectors

Application of Hilti shear connectors

15

Scope of the lecture

Basic principles of the composite structures
Shear connectors
Composite beams
Composite columns
Steel-concrete slabs

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8
Composite beams

Composite beam with concrete slab

Composite beam cast in the corrugated sheet

Shear connectors to avoid slip

between steel beam and concrete slab

17

Effective cross section

The stress in the concrete slab is not uniform because of effect of shear lag
Idealized stress distribution (i.e. uniform stress on the effective width beff)
is considered in the concrete slab
Considering imply supported beams, the effective width beff is equal to
L
beff 
4
Idealized stress
in the concrete

Real stress
distribution in the
concrete slab

Effective width of the concrete slab

Stress distribution in the concrete slab 18

9
Classification of cross sections
Beam flange connected to the concrete slab by shear connectors
is assumed to be fully stabilized - no local buckling of the flange can
occur – Class 1 for any c/t ratio
The other parts are classified in similar way as normal steel beams

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Resistance of the beam

Two cases should be distinguished:
 Full shear connection
(the shear connection is not critical part of the beam)
 This is the preferable way of design
 Partial shear connection
(shear connection limits the resistance of the beam)
 It is used in cases when the number of the connectors required for full shear
connection does not fit on the beam and smaller number of the connectors
must be used
 Stiffness of the beam decrease - deformation increase

Check of cross section – plastic stress distribution at ULS (full shear connection)
 Positive plastic bending moment capacity is evaluated with one of the
following options
 Neutral axis in the slab
 Neutral axis in the beam
 Negative plastic moment capacity needs to be evaluated at supports of
continuous beams, etc. 20

10
Plastic bending moment capacity

Full shear connection

Assumption: neutral axis is in the concrete slab
Force equilibrium equation to get the depth of concrete zone in compression
Fc  Fa
f ck fy
beff x 0,85  Aa  x  ... but x must be smaller than depth of the slab
c a
Moment equilibrium equation to get the bending moment capacity

M pl , Rd  Fa r  Fc r
21

Plastic bending moment capacity

Full shear connection

Assumption: neutral axis is in the steel section
Force equilibrium equation to get the depth of concrete zone in compression

Fc  Fa1  Fa 2  x  ... (limits for x exist)

Moment equilibrium equation to get the bending moment capacity

 d  d
M pl , Rd  Fc  ha 2    Fa1  ha1  
 2  2 22

11
Criteria to be checked
Ultimate Limit States
 Moment resistance of critical cross section
 Resistance in shear
 Resistance in longitudinal shear (resistance of shear connectors)

Serviceability Limit States

 Elastic behaviour
 Deflections

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Resistance in shear
See shear resistance of steel beams
The concrete slab has no effect on the shear resistance
Av f y
V pl , Rd 
3 M0

Av shear area = area of the beam web

Shear area of I sections

24

12
Shear connection
Shear connectors transfer longitudinal shear V
Ductile shear connectors: the connectors can be uniformly distributed
 Shear force to be transferred by connectors
f ck
Fcf  Ac 0,85
c
 Number of connectors on half-span:
Fcf
nf 
PRd

a a a a a a

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Shear connection
Shear connectors transfer longitudinal shear V
Non-ductile connectors: the connectors follow shear force distribution
V S
V  Ed c
Ii
VEd shear force on the beam,
Si static moment of effective cross section of slab
to the centre of gravity of the beam,
Ii moment of inertia of the beam

a1 a2 a3 a4 a5

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13
Serviceability limit states
Service load is assumed for the calculations (G = Q = 1,0; M = 1,0)

Beam is in elastic stage – this should be checked by calculating the

maximum stress in the steel and concrete and comparing it to the yield
limit of steel and to the concrete strength

Deflections

Cracking of concrete (limit of crack width)

Limit crack width wk = 0,3 mm
This is controlled by the slab reinforcement

The assembling procedure has significant effect on both the stress and the
deflection of the beam

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Elastic behaviour
Assumption of Navier’s hypothesis (planar cross-section after deformation)
 Components and maximum stress
 Concrete (0,85 fck / c )
 Steel (fy / M0)
 Reinforcement (fsk / s)

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14
Properties of idealized cross section
Concrete slab is transformed to the equivalent steel part
The ratio at which the dimensions are modified is
Ea
n
0,5 Ecm

Ea is modulus of elasticity of steel

Ecm is modulus of elasticity of concrete, the factor 0,5 is used to take into
account the creep in a simplified way

 Area of cross section Ai

A
Ai  Aa  c  As
n
 Centre of gravity
 Moment of inertia Ii
I y ,i  ....... Idealized section
of composite beam
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Assembling procedure
Has influence on deformation and elastic stress distribution
(but not on Mpl,Rd)
Two procedures can be used
 Without scaffolding
Two stages need to be considered:
 the assembly stage, when steel beam is loaded by weight of fresh concrete (and
some temporary load presented at the assembling) - no composite action
 the final stage, when the concrete is hard and ready to carry the load - the composite
beam has to carry all the load
In elastic calculation, the stress from the assembly stage (from the weight of the
fresh concrete) and from the remaining load (other dead load applied after the
concrete gets hard and from variable load) add
 On scaffolding
The weight of the fresh concrete is supported by temporary structure -
scaffolding, therefore no stresses and deformation occur, all the load is resisted
by the composite beam

30

15
Assembling with scaffolding
Stresses, deflections
Stress at upper edge of the concrete slab
1 M Ek zc
c   c  f c ,k
n I y ,i

Stress at lower edge of steel section

M z
 a  Ek a a  fy
I y ,i

Deformation (for simply supported beam with uniformly distributed load)

5 vk l 4

384 Ea I y ,i
Note: easy method for the design
saves the steel - the beams are smaller as only the composite beam is loaded
cheap? - consider the price of rent and erection of the scaffolding
effective for large spans, i.e. spans exceeding 7 m
31

Assembling without scaffolding

Stresses
Assebling stage
The load at assembly should be considered, i.e. self weight of the beam, weight of the fresh
concrete and people working with the concrete
Stress in the steel section (top and bottom edges) σ 1
No stress
M z in the concrete
 a1  Ek .1  a1  f y
Iy
z
z

Final stage
The remaining load should be considered, i.e. the floor and ceiling and any
variable load
Stress in the steel section (bottom edge)
M Ek .2 za
 a2 
I y ,i
Stress in the concrete (top surface
of the slab)
1 M Ek .2 zc
c 
n I y ,i
32

16
Assembling with scaffolding
Stresses
Total stress
The total stress is obtained as the sum of the previous
Stress in the steel section (bottom edge) σ1 σ2
No stress
 a   a1   a 2 in the concrete

zc
z
Stress in the concrete (top surface of the slab)

za
 c  0   c2

z
Note: more complicated method for the design (two situations need to be considered)
the beams are bigger - usually the assembling stage limits the size of the steel beam
effective for small spans, i.e. spans up to 7 m

33

Assembling with scaffolding

Deformation
Deformation (for simply supported beam with uniformly distributed load)
At assembly stage
The load at assembly should be considered, i.e. self weight of the beam, weight of the fresh
concrete and people working with the concrete
The moment of inertia of the steel section only (Iy) is used
5 vk 1 l 4
1 
384 Ea I y
At final stage
The remaining load should be considered, i.e. the floor and ceiling and any variable load
The moment inertia of the composite beam (Iy,i) is used
5 vk 2 l 4
2 
384 Ea I y ,i
Total deformation
The total stress is obtained as the sum of the previous
  1   2

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17
Scope of the lecture
Basic principles of the composite structures
Shear connectors
Composite beams
Composite columns
Steel-concrete slabs

35

Columns
Fully encased columns
Partially encased columns
Concrete filled hollow sections (circular, rectangular)

36

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Columns

37

Simplified method of
resistance evaluation of columns
Criteria
 Columns with double-symmetric steel sections
 Constant section along length

Aa fy a 
 0,2 <  < 0,9, where  
N pl ,Rd

 0,2 < hc/bc < 5,0

 Relative slenderness of column   2 ,0

 Area of the reinforcement should be max. 6 % of concrete area

38

19
Centric compression
Full plastification of all parts

 fy   0 ,85 f ck   f sk 
N pl .Rd  Aa    Ac    As  
a   c   s 
Concrete filled hollow sections
... use fck instead of 0,85 fck
Increase of concrete strength confined by the steel section

39

Buckling resistance

N Ed   N pl .Rd

 ... reduction factor (buckling factor) as for steel members

Use buckling curves a, b, c
N pl .Rd

N cr

40

20
Critical load of composite element
 2 EI e
N cr 
2

Bending stiffness
EI e  Ea I a  0,6 Ecm I c  Es I s
 buckling length
Ea  Es modulus of elasticity of steel
Ecm modulus of elasticity of concrete
Ia, Ic, Is moments of inertia of steel part, concrete part
and reinforcement to the centroidal axis

41

Compression and bending

Interaction curve for combined MEd + NEd

42

21
Joints of composite structures
Joints are encased in concrete afterwards (to maintain the same fire resistance
of the joints as of the other parts)

43

Scope of the lecture

Basic principles of the composite structures
Shear connectors
Composite beams
Composite columns
Steel-concrete slabs

44

22
Concrete slab cast on corrugated steel sheets

 Corrugated sheet filled by concrete

1. Fresh concrete = assembling stage: load to sheet
2. After hardening of concrete: sheet = reinforcement
(plus standard reinforcement when necessary )
 For static loading

45

Concrete slabs cast on corrugated steel sheets

Shear connection
 mechanical connection assured by nops or profiling in sheet
 frictional connection of profiles with self locking shape profiles
 end stop by welded studs
 end stop by deformed ribs of self locking shape profiles

Mechanical connection Frictional connection

Shear connection End connection

46

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 Slip between steel and concrete

47

Thank you for your attention

48

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