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Material
Steel A36
Concrete 4000 psi
Project item baseplate
Design
Name baseplate
Description
Analysis Stress, strain/ simplified loading
Design code AISC - LRFD 2016
Beams and columns
β – Direction γ - Pitch α - Rotation Offset ex Offset ey Offset ez
Name Cross-section Forces in
[°] [°] [°] [mm] [mm] [mm]
COL 2 - HEA300A 0.0 -90.0 0.0 0 0 0 Node
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Cross-sections
Name Material
2 - HEA300A A36
Cross-sections
Name Material Drawing
2 - HEA300A A36
Anchors
Diameter fu Gross area
Name Bolt assembly
[mm] [MPa] [mm2]
5/8 A307 5/8 A307 16 414.0 198
Load effects (equilibrium not required)
N Vy Vz Mx My Mz
Name Member
[kN] [kN] [kN] [kNm] [kNm] [kNm]
LE1 COL 94.0 35.0 0.0 0.0 0.0 0.0
Foundation block
Item Value Unit
CB 1
Dimensions 820 x 823 mm
Depth 500 mm
Anchor 5/8 A307
Anchoring length 300 mm
Shear force transfer Anchors
Check
Summary
Name Value Check status
Analysis 100.0% OK
Plates 0.0 < 5.0% OK
Anchors 84.9 < 100% OK
Welds 13.7 < 100% OK
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Concrete block Not calculated
Buckling Not calculated
Plates
fy Thickness σEd εPl σcEd
Name Loads Check status
[MPa] [mm] [MPa] [%] [MPa]
COL-bfl 1 248.2 10.5 LE1 47.2 0.0 0.0 OK
COL-tfl 1 248.2 10.5 LE1 47.2 0.0 0.0 OK
COL-w 1 248.2 7.5 LE1 49.5 0.0 0.0 OK
BP1 248.2 20.0 LE1 90.9 0.0 0.0 OK
Design data
fy εlim
Material
[MPa] [%]
A36 248.2 5.0
Symbol explanation
εPl Plastic strain
σcEd Contact stress
σEd Eq. stress
fy Yield strength
εlim Limit of plastic strain
Overall check, LE1
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Strain check, LE1
Equivalent stress, LE1
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Anchors
Nf V ϕNcbg ϕVcbg ϕVcp Utt Uts Utts
Shape Item Loads Status
[kN] [kN] [kN] [kN] [kN] [%] [%] [%]
A1 LE1 23.6 8.7 174.9 55.0 324.9 55.8 63.7 84.9 OK
A2 LE1 23.4 8.8 174.9 - 324.9 55.5 37.3 56.8 OK
A3 LE1 23.6 8.7 174.9 55.0 324.9 55.8 63.7 84.9 OK
A4 LE1 23.4 8.8 174.9 - 324.9 55.5 37.3 56.8 OK
Design data
ϕNsa ϕVsa
Grade
[kN] [kN]
5/8 A307 - 1 42.3 23.5
Symbol explanation
Nf Tension force
V Resultant of shear forces Vy, Vz in bolt
ϕNcbg Concrete breakout strength in tension – ACI 318-14 – 17.4.2
ϕVcbg Concrete breakout strength in shear – ACI 318-14 – 17.5.2
ϕVcp Concrete pryout strength in shear – ACI 318-14 – 17.5.3
Utt Utilization in tension
Uts Utilization in shear
Utts Utilization in tension and shear
ϕNsa Steel strength of anchor in tension - ACI 318-14 – 17.4.1
ϕVsa Steel strength of anchor in shear - ACI 318-14 – 17.5.1
Weld sections
Th Ls L Lc Fn ϕRn Ut
Item Edge Xu Loads Status
[mm] [mm] [mm] [mm] [kN] [kN] [%]
BP1 COL-bfl 1 E70xx ◢7.1◣ ◢10.0◣ 299 20 LE1 4.4 32.5 13.6 OK
E70xx ◢7.1◣ ◢10.0◣ 299 20 LE1 4.2 31.2 13.6 OK
BP1 COL-tfl 1 E70xx ◢7.1◣ ◢10.0◣ 299 20 LE1 4.2 31.3 13.4 OK
E70xx ◢7.1◣ ◢10.0◣ 299 20 LE1 4.4 32.5 13.7 OK
BP1 COL-w 1 E70xx ◢7.1◣ ◢10.0◣ 271 21 LE1 4.9 48.0 10.2 OK
E70xx ◢7.1◣ ◢10.0◣ 271 21 LE1 5.0 48.0 10.3 OK
Symbol explanation
Th Throat thickness of weld
Ls Leg size of weld
L Length of weld
Lc Length of weld critical element
Fn Force in weld critical element
ϕRn Weld resistance AISC 360-16 J2.4
Ut Utilization
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Concrete block
A1 A2 σ Ut
Item Loads Status
[mm2] [mm2] [MPa] [%]
CB 1 LE1 NaN NaN - - OK
Symbol explanation
A1 Loaded area
A2 Supporting area
σ Average stress in concrete
Ut Utilization
Buckling
Buckling analysis was not calculated.
Code settings
Item Value Unit Reference
Friction coefficient - concrete 0.40 - ACI 349 – B.6.1.4
Friction coefficient in slip-resistance 0.30 - AISC 360-16 J3.8
Limit plastic strain 0.05 -
Plastic
Weld stress evaluation
redistribution
Detailing No
Distance between bolts [d] 2.66 - AISC 360-16 – J3.3
Distance between bolts and edge [d] 1.25 - AISC 360-16 – J.3.4
Concrete breakout resistance check Both
Base metal capacity check at weld
No AISC 360-16: J2-2
fusion face
Cracked concrete Yes ACI 318-14 – Chapter 17
Local deformation check No
Local deformation limit 0.03 - CIDECT DG 1, 3 - 1.1
Analysis with large deformations for hollow
Geometrical nonlinearity (GMNA) Yes
section joints
Theoretical Background
CBFEM versus AISC 360
The weak point of standard design method is in analyzing of internal forces and stress in a joint.
CBFEM replaces specific analysis of internal forces in joint with general FEA.
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Check methods of specific components like bolts or welds are done according to standard AISC
360.
For the fasteners – bolts and welds – special FEM components had to be developed to model the
welds and bolts behaviour in the connection. All parts of 1D members and all additional plates are
modeled as plate/walls. These elements are made of steel (metal in general) and the behaviour of
this material is significantly nonlinear.
The real stress-strain diagram of steel is replaced by the ideal plastic material for design purposes
in building practice. The advantage of ideal plastic material is, that only yield strength and modulus
of elasticity must be known to describe the material curve. The yield strength is multiplied by
resistance factor (LRFD) or divided by safety factor (ASD) – AISC 360, Appendix 1. The granted
ductility of construction steel is 15 %. The real usable value of limit plastic strain is 5% for ordinary
design (EN 1993-1-5 appendix C paragraph C.8 note 1).
The stress in steel cannot exceed the yield strength when using the ideal elastic-plastic stress-
strain diagram.
Real tension curve and the ideal elastic-plastic diagram of material
CBFEM method aims to model the real state precisely. Meshes of plates / walls are not merged,
no intersections are generated between them, unlike it is used to when modeling structures and
buildings. Mesh of finite elements is generated on each individual plate independently on mesh of
other plates.
Between the meshes, special massless force interpolation constraints are added. They ensure the
connection between the edge of one plate and the surface or edge of the other plate.
This unique calculation model provides very good results – both for the point of view of precision
and of the analysis speed. The method is protected by patent.
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The steel base plate is placed loosely on the concrete foundation. It is a contact element in the
analysis model – the connection resists compression fully, but does not resist tension.
Stress-strain diagram of contact between the concrete block and the base plate
The concrete block in CBFEM is modeled using Winkler-Pasternak subsoil model. The stiffness of
subsoil is determined using modulus of elasticity of concrete and effective height of subsoil. The
concrete block is not designed by CBFEM method.
Welds are modeled using a special elastoplastic element, which is added to the interpolation links
between the plates. The element respects the weld throat thickness, position and orientation. The
plasticity state is controlled by stresses in the weld throat section. The plastic redistribution of
stress in welds allows for stress peaks to be redistributed along the longer part of the weld.
Bolted connection consists of two or more clasped plates and one or more bolts. Plates are placed
loosely on each other.
A contact element is inserted between plates in the analysis model, which acts only in
compression. No forces are carried in tension.
Shear force is taken by bearing. Special model for its transferring in the force direction only is
implemented. IDEA StatiCa Connection can check bolts for interaction of shear and tension. The
bolt behavior is implemented according to the following picture.
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Bolt – tension
Symbols explanation:
• K – linear stiffness of bolt,
• Kp – stiffness of bolt at plastic branch,
• Flt – limit force for linear behaviour of bolt,
• Ft,Rd – limit bolt resistance,
• ul – limit deformation of bolt.
Bolt – interaction of shear and tension
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Loads
End forces of member of the frame analysis model are transferred to the ends of member
segments. Eccentricities of members caused by the joint design are respected during load transfer.
The analysis model created by CBFEM method corresponds to the real joint very precisely,
whereas the analysis of internal forces is performed on very idealised 3D FEM bar model, where
individual beams are modeled using centrelines and the joints are modeled using immaterial
nodes.
Joint of a vertical column and a horizontal beam
Internal forces are analysed using 1D members in 3D model. There is an example of courses of
internal forces in the following picture.
Internal forces in horizontal beam. M and V are the end forces at joint.
The effects caused by member on the joint are important to design the connection. The effects are
illustrated in the following picture.
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Effects of the member on the joint. CBFEM model is drawn in dark blue color.
Moment M and shear force V act in a theoretical joint. The point of theoretical joint does not exist in
CBFEM model, thus the load cannot be applied here. The model must be loaded by actions M and
V, which have to be transferred to the end of segment in the distance r.
Mc = M − V · r
Vc = V
In CBFEM model, the end section of segment is loaded by moment Mc and force Vc.
Welds
Fillet welds
The design strength, ϕRn and the allowable strength, Rn/Ω of welded joints are evaluated in
connection weld check.
ϕ = 0.75 (LRFD)
Ω = 2.00 (ASD)
Available strength of welded joints is evaluated according to AISC 360 – J2.4:
Rn = FnwAwe
Fnw = 0.60 FEXX (1.0 + 0.50 sin1.5Θ)
where
• Fnw – nominal stress of weld material,
• Awe – effective area of the weld,
• FEXX – electrode classification number, i.e., minimum specified tensile strength,
• Θ – angle of loading measured from the weld longitudinal axis.
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For long welds and welding to unstiffened flanges or webs of rectangular hollow sections, the weld
material model is fine-tuned so that no reduction factor is necessary. The weld resistance is
governed by most stressed weld element.
CJP groove welds
AISC Specification Table J2.5 identifies four loading conditions that might be associated with JP
groove welds, and shows that the strength of the joint is either controlled by the base metal or that
the loads need not be considered in the design of the welds connecting the parts. Accordingly,
when CJP groove welds are made with matching-strength filler metal, the strength of a connection
is governed or controlled by the base metal, and no checks on the weld strength are required.
Bolts
Tensile and shear strength of bolts
The design tensile or shear strength, ϕRn, and the allowable tensile or shear strength, Rn / Ω of a
snug-tightened bolt is determined according to the limit states of tension rupture and shear rupture
as follows:
Rn = FnAb
ϕ = 0.75 (LRFD)
Ω = 2.00 (ASD)
where
• Ab – nominal unthreaded body area of bolt or threaded part,
• Fn – nominal tensile stress, Fnt, or shear stress, Fnv, from Table J3.2.
The tensile force, against which the required tensile strength is checked, includes any tension
resulting from prying action produced by deformation of the connected parts.
Combined Tension and shear in bearing type connection
The available tensile strength of a bolt subjected to combined tension and shear is determined
according to the limit states of tension and shear rupture as follows:
Rn = F'ntAb (AISC 360 J3-2)
ϕ = 0.75 (LRFD)
Ω = 2.00 (ASD)
F'nt = 1.3 Fnt − frvFnt / ϕFnv (AISC 360 J3-3a LRFD)
F'nt = 1.3 Fnt − frvΩ Fnt / Fnv (AISC 360 J3-3b ASD)
where
• F'nt – nominal tensile stress modified to include the effects of shear stress,
• Fnt – nominal tensile stress from AISC 360 – Tab. J3.2,
• Fnv – nominal shear stress from AISC 360 – Tab. J3.2,
• frv – required shear stress using LRFD or ASD load combinations. The available shear
stress of the fastener shall be equal or exceed the required shear stress, frv.
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Bearing strength in bolt holes
The available bearing strength, ϕRn and Rn/Ω at bolt holes is determined for the limit state of
bearing as follows:
For a bolt in a connection with standard holes:
Rn = 1.2 lctFu ≤ 2.4 d t Fu (AISC 360 J3-6a, c)
For a bolt in a connection with slotted holes:
Rn = 1.0 lct Fu ≤ 2.0 d t Fu (AISC 360 J3-6e, f)
ϕ = 0.75 (LRFD)
Ω = 2.00 (ASD)
where
• Fu – specified minimum tensile strength of the connected material,
• d – nominal bolt diameter,
• lc – clear distance, in the direction of the force, between the edge of the hole and the edge
of the adjacent hole or edge of the material,
• t – thickness of connected material.
Preloaded bolts
The design slip resistance of a preloaded class A325 or A490 bolt with of effect of tensile force,
Ft,Ed according to AISC 360 – J3.9.
Preloading force to be used AISC 360 – Tab. J3.1.
Tb = 0.7 fubAs
Design slip resistance per bolt AISC 360 – J3.8
Rn = 1.13 μ TbNs
Utilisation in shear [%]:
Uts = V / Rn
where
• As – tensile stress area of the bolt,
• fub – ultimate tensile strength,
• μ – mean slip factor coefficient,
• Ns – number of the friction surfaces. Check is calculated for each friction surface separately,
• V – shear force.
Anchors
The anchor bolt element is elastic-plastic with significant strain hardening. The maximum steel
tensile resistance is expected at the strain which equals to 0.25 × guaranteed elongation. The
failure mode due to concrete cracking may occur before the anchor steel tensile resistance is
reached and is considered as a completely brittle failure.
Similarly, the steel components in shear (anchor bolt, base plate in bearing) are able to yield but
failure modes connected with concrete cracking may occur suddenly as a brittle failure.
All standards use Concrete Capacity Design method developed by prof. R. Eligehausen at
University of Stuttgart. The theory is based on vast experimental and numerical testing mostly on
unreinforced concrete blocks and relatively short, often post-installed, anchors.
Anchorage is designed according to ACI 318-14 – Chapter 17. The design is available only for
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LRFD. Some failure modes (e.g. steel resistance) are evaluated for single anchors, others (e.g.
concrete breakout) are checked for group of anchors.
