5
Check of components according to AISC
CBFEM method combines the advantages of general Finite Element Method and standard Component Method. The stresses and internal forces calculated on the accurate CBFEM model are used in checks of all components.
Individual components are checked according to American Institute of Steel Construction (AISC) 36016.
5.1 Plates
The resulting equivalent stress (HMH, von Mises) and plastic strain are calculated on plates. When the yield strength (in LRFD multiplied by material resistance factor ϕ = 0.9, in ASD divided by material safety factor Ω = 1.67, which are editable in Code setup) on the bilinear material diagram is reached, the check of the equivalent plastic strain is performed. The limit value of 5 % is suggested in Eurocode (EN199315 App. C, Par. C8, Note 1). This value can be modified in Code setup but verification studies were made for this recommended value.
Plate element is divided into 5 layers and elastic/plastic behavior is investigated in each of them. The program shows the worst result from all of them.
The CBFEM method can provide stress a little bit higher than yield strength. The reason is the slight inclination of the plastic branch of the stressstrain diagram, which is used in the analysis to improve the stability of the interaction calculation. This is not a problem for practical design. The equivalent plastic strain is exceeded at higher stress and the joint does not satisfy anyway.
5.2 Welds
5.2.1 Fillet welds
The design strength, ϕR_{n}, and the allowable strength, R_{n}/Ω, of welded joints are evaluated in the connection weld check.
ϕ = 0.75 (Load and Resistance Factor Design, LRFD, editable in Code setup)
Ω = 2.00 (Allowable Strength Design, ASD, editable in Code setup)
Available strength of welded joints is evaluated according to AISC 36016 – J2.4
R_{n} = F_{nw} A_{we}
F_{nw} = 0.6 F_{EXX} (1.0 + 0.5 sin^{1.5}θ )
where:
 F_{nw} – nominal stress of weld material
 A_{we} – effective area of the weld
 F_{EXX} – electrode classification number, i.e., minimum specified tensile strength
 θ – angle of loading measured from the weld longitudinal axis, degrees
Base metal strength is evaluated if the option is selected in Code setup (Base metal capacity at the fusion face).
R_{n} = F_{nBM} A_{BM} – AISC 36016 – J2.4 (J22)
where:
 F_{nBM} = 0.6 F_{u} – nominal strength of the base metal – AISC 36016 – J4.2 (J44)
 – crosssectional area of the base metal
 F_{u} – specified minimum tensile strength
All values required for check are printed in tables.
5.2.2 CJP groove welds
AISC Specification Table J2.5 identifies four loading conditions that might be associated with 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 Complete Joint Penetration (CJP) groove welds are made with matchingstrength filler metal, the strength of a connection is governed or controlled by the base metal and no checks on the weld strength are required.
5.3 Bolts
5.3.1 Tensile and shear strength of bolts
The design tensile or shear strength, ϕR_{n}, and the allowable tensile or shear strength, R_{n}/Ω of a snugtightened bolt is determined according to the limit states of tension rupture and shear rupture as follows:
R_{n} = F_{n}A_{b}
ϕ = 0.75 (LRFD, editable in Code setup)
Ω = 2.00 (ASD, editable in Code setup)
where:
A_{b} – nominal unthreaded body area of bolt or threaded part
F_{n} – nominal tensile stress, F_{nt}, or shear stress, F_{nv}, from Table J3.2
The required tensile strength includes any tension resulting from prying action produced by the deformation of the connected parts.
5.3.2 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:
R_{n} = F'_{nt} A_{b} (AISC 36016 J32)
ϕ = 0.75 (LRFD, editable in Code setup)
Ω = 2.00 (ASD, editable in Code setup)
(AISC 36016 J33a LRFD)
(AISC 36016 J33b ASD)
where:
 F'_{nt} – nominal tensile stress modified to include the effects of shear stress
 F_{nt} – nominal tensile stress from AISC 36016 Table J3.2
 F_{nv} – nominal shear stress from AISC 36016 Table J3.2
 f_{rv} – 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, f_{rv}
5.3.3 Bearing strength in bolt holes
The available bearing strengths, ϕR_{n} and R_{n}/Ω, at bolt holes are determined for the limit state of bearing as follows:
ϕ = 0.75 (LRFD, editable in Code setup)
Ω = 2.00 (ASD, editable in Code setup)
The nominal bearing strength of the connected material, R_{n}, is determined as follows:
For a bolt in a connection with standard holes:
R_{n} = 1.2 l_{c}t F_{u} ≤ 2.4 d t F_{u} (AISC 36016 J36a, J36a, c)
For a bolt in a connection with slotted holes:
R_{n} = 1.0 l_{c}t F_{u} ≤ 2.0 d t F_{u} (AISC 36016 J36a, J36e, f)
where:
 F_{u} – specified minimum tensile strength of the connected material
 d – nominal bolt diameter
 l_{c} – 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 the connected material
5.4 Preloaded bolts
The design slip resistance of preloaded class A325 or A490 bolt with the effect of tensile force Ft
Preloading force to be used AISC 36010 tab. J3.1.
T_{b} = 0.7 f_{ub} A_{s}
Design slip resistance per bolt AISC 36010 par. J3.8
R_{n} = k_{SC} μ D_{u}h_{f} T_{b} n_{s}
Utilization in shear [%]:
U_{ts} = V / ϕR_{n} (LRFD)
U_{ts} = Ω V / R_{n} (ASD)
where:
 A_{s} – tensile stress area of the bolt
 f_{ub} – ultimate tensile strength
 – factor for combined tension and shear (LRFD) (J35a)
 – factor for combined tension and shear (ASD) (J35b)
 μ – mean slip factor coefficient editable in Code setup
 D_{u} = 1.13 – multiplier that reflects the ratio of the mean installed bolt pretension to the specified minimum bolt pretension
 h_{f} = 1.0 – factor for fillers
 n_{s} – number of the friction surfaces; Check is calculated for each friction surface separately
 V – shear force acting on the bolt
 ϕ = 1.0 – resistance factor for standard size holes (LRFD) editable in Code setup
 ϕ = 0.7 – resistance factor for slotted holes (LRFD)
 Ω = 1.5 – resistance factor for standard size holes (ASD) editable in Code setup
 Ω = 2.14 – resistance factor for slotted holes (ASD)
5.5 Concrete in compression
Concrete design bearing strength in compression is designed according to AISC 36016, Section J8. When the supported surface of the concrete is larger than the base plate the design bearing strength is defined as
where:
The assessment of concrete in bearing is as follows σ ≤ ϕ_{c} f_{p(max)} for LRFD σ ≤ f_{p(max)} / Ω_{c} for ASD where:

5.6 Transfer of shear forces
Shear loads can be transferred via one of these options:
 Shear lug,
 Friction,
 Anchor bolts.
5.6.1 Shear lug
Only LFRD is available. The shear load is transferred via the shear lug. The concrete in bearing and, unless reinforcement is provided to develop the required strength, concrete breakout checks are necessary.
The bearing capacity of shear lug against concrete is determined according to ACI 34901 – B.4.5 and ACI 34901 RB11 as:
ϕP_{br} = ϕ 1.3 f'_{c} A_{1} + ϕ K_{c} (N_{y} – P_{a})
where:
 ϕ = 0.7 – strength reduction factor for bearing on concrete according to ACI 349
 f'_{c} – concrete compressive strength
 A_{1} – projected area of the embedded shear lug in the direction of the force excluding the portion of the lug in contact with the grout above concrete member
 K_{c} = 1.6 – confinement coefficient
 N_{y} = n A_{se} F_{y} – yield strength of tensioned anchors
 P_{a} – external axial load
The concrete breakout strength of the shear lug according to ACI 349 – B11 is:
where:
If the concrete breakout resistance in Code setup is disabled, user is provided with the force that needs to be transferred via reinforced concrete. 
5.6.2 Friction
The shear load is transferred via friction. The shear resistance is determined as:
ϕ_{c} V_{r} = ϕ_{c} μ C (LRFD)
V_{r} / Ω_{c} =μ C / Ω_{c} (ASD)
where:
 ϕ_{c} = 0.65 – resistance factor (LRFD)
 Ω_{c} = 2.31 – safety factor (ASD)
 μ = 0.4 – coefficient of friction between base plate and concrete (recommended value 0.4 in AISC Design guide 7 – 9.2 and ACI 349 – B.6.1.4, editable in Code setup)
 C – compressive force
5.6.3 Anchor bolts
If the shear load is transferred via anchor bolts only, the shear force acting on each anchor is determined by FEA and anchor bolts are assessed according to ACI 31814 as described in following chapters.
5.7 Anchors
Only LFRD is available. Anchor rods are designed according to AISC 36016 – J9 and ACI 31814 – Chapter 17. The following resistances of anchor bolts are evaluated:
 Steel strength of anchor in tension ϕN_{sa},
 Concrete breakout strength in tension ϕN_{cbg},
 Concrete pullout strength ϕN_{p},
 Concrete sideface blowout strength ϕN_{sb},
 Steel strength of anchor in shear ϕV_{sa},
 Concrete breakout strength in shear ϕV_{cbg},
 Concrete pryout strength of anchor in shear ϕV_{cp}.
The user must choose the concrete condition (cracked or noncracked – with no cracks in service condition) and the type of anchors (with or without washer plates).
5.7.1 Steel strength of anchor in tension
Steel strength of anchor in tension is determined according to ACI 31814 – 17.4.1 as
ϕN_{sa} = ϕ A_{se,N} f_{uta}
where:
 ϕ = 0.7 – strength reduction factor for anchors in tension according to ACI 31814 – 17.3.3, the factor is editable in Code setup
 A_{se,N} – tensile stress area
 f_{uta} – specified tensile strength of anchor steel and shall not be greater than 1.9 f_{ya} and 120 ksi
5.7.2 Concrete breakout strength
Concrete breakout strength is designed according to the Concrete Capacity Design (CCD) in ACI 31814 – Chapter 17. In the CCD method, the concrete cone is considered to be formed at an angle of approximately 34° (1 vertical to 1.5 horizontal slope). For simplification, the cone is considered to be square rather than round in plan. The concrete breakout stress in the CCD method is considered to decrease with an increase in size of the breakout surface. Consequently, the increase in strength of the breakout in the CCD method is proportional to the embedment depth to the power of 1.5. Anchors whose concrete cones overlap create a group of anchors which create a common concrete cone. Note that no equivalent ASD solution exists for concrete capacity design.
where:
 ϕ = 0.7 – strength reduction factor for anchors in tension according to ACI 31814 – 17.3.3, the factor is editable in Code setup
 A_{Nc} – actual concrete breakout cone area for a group of anchors that create common concrete cone
 A_{Nco} = 9 h_{ef}^{2} – concrete breakout cone area for single anchor not influenced by edges
 – modification factor for anchor groups loaded eccentrically in tension; in the case where eccentric loading exists about two axes, the modification factor Ψ_{ec,N} is calculated for each axis individually and the product of these factors is used
 – modification factor for edge distance
 c_{a,min} – smallest distance from the anchor to the edge
 Ψ_{c,N} – modification factor for concrete conditions; Ψ_{c,N} =1 for cracked concrete, Ψ_{c,N} =1.25 for noncracked concrete
 Ψ_{cp,N} = min (c_{a,min} / c_{ac},1) – modification factor for splitting for postinstalled anchors designed for uncracked concrete without supplementary reinforcement to control splitting; Ψ_{cp,N} = 1 for all other cases
 – basic concrete breakout strength of a single anchor in tension in cracked concrete; for castin anchors and 11 in. ≤ h_{ef} ≤ 25 in.
 k_{c} = 24 for castin anchors
 h_{ef} – depth of embedment; according to Chapter 17.4.2.3 in ACI 31814, the effective embedment depth h_{ef} is reduced to if anchors are located less than 1.5 h_{ef} from three or more edges
 s – spacing between anchors
 c_{a,max} – maximum distance from an anchor to one of the three close edges
 λ_{a} = 1 – modification factor for lightweight concrete
 f'_{c} – concrete compressive strength [psi]
According to ACI 31814 – 17.4.2.8, in case of headed anchors, the projected surface area A_{Nc} is determined from the effective perimeter of the washer plate, which is the lesser value of d_{a} + 2 t_{wp} or d_{wp}, where:
 d_{a} – anchor diameter
 d_{wp} – washer plate diameter or edge size
 t_{wp} – washer plate thickness
The group of anchors is checked against the sum of tensile forces in anchors loaded in tension and creating a common concrete cone.
According to ACI 31814 – 17.4.2.9, where anchor reinforcement is developed in accordance with ACI 31814 – 25 on both sides of the breakout surface, the anchor reinforcement is presumed to transfer the tension forces and concrete breakout strength is not evaluated.
5.7.3 Concrete pullout strength
Concrete pullout strength of an anchor is defined in ACI 31814 – 17.4.3 as
ϕN_{pn} = ϕΨ_{c,P} N_{p}
where:
 ϕ = 0.7 – strength reduction factor for anchors in tension according to ACI 31814 – 17.3.3, editable in Code setup
 Ψ_{c,P} – modification factor for concrete condition; Ψ_{c,P} = 1.0 for cracked concrete, Ψ_{c,P} = 1.4 for noncracked concrete
 N_{P} = 8 A_{brg} f'_{c} for headed anchor
 A_{brg} – bearing area of the head of stud or anchor bolt
 f'_{c} – concrete compressive strength
Concrete pullout strength for other types of anchors than headed is not evaluated in the software and has to be specified by the manufacturer.
5.7.4 Concrete sideface blowout strength
Concrete sideface blowout strength of headed anchor in tension is defined in ACI 31814 – 17.4.4 as
The concrete sideface blowout strength is multiplied by one of reduction factors:
where:
 ϕ = 0.7 – strength reduction factor for anchors in tension according to ACI 31814 – 17.3.3, editable in Code setup
 c_{a1} – shorter distance from the centreline of an anchor to an edge
 c_{a2} – longer distance, perpendicular to c_{a1}, from the centreline of an anchor to an edge
 A_{brg} – bearing area of the head of stud or anchor bolt
 f'_{c} – concrete compressive strength
 h_{ef} – depth of embedment; according to Chapter 17.4.2.3 in ACI 31814, the effective embedment depth h_{ef} is reduced to if anchors are located less than 1.5 h_{ef} from three or more edges
 s – spacing between two adjacent anchors near one edge
5.7.5 Steel strength in shear
The steel strength in shear is determined according to ACI 31814 – 17.5.1 as
ϕV_{sa} = ϕ 0.6 A_{se,V} f_{uta}
where:
 ϕ = 0.65 – strength reduction factor for anchors in tension according to ACI 31814 – 17.3.3, editable in Code setup
 A_{se,V} – tensile stress area
 f_{uta} – specified tensile strength of anchor steel and shall not be greater than 1.9 f_{ya} and 120 ksi
If mortar joint is selected, steel strength in shear V_{sa} is multiplied by 0.8 (ACI 31814 – 17.5.1.3).
The shear on lever arm, which is present in case of base plate with oversized holes and washers or plates added to the top of the base plate to transmit the shear force, is not considered.
5.7.6 Concrete breakout strength of anchor in shear
Concrete breakout strength of an anchor or anchor group in shear is designed according to ACI 318 14 – 17.5.2.
where:
 ϕ = 0.65 – strength reduction factor for anchors in shear according to ACI 31814 – 17.3.3, editable in Code setup
 A_{v} – projected concrete failure area of an anchor or group of anchors
 A_{vo} – projected concrete failure area of one anchor when not limited by corner influences, spacing or member thickness
 – modification factor for anchor groups loaded eccentrically in shear
 – modification factor for edge effect
 Ψ_{c,V} – modification factor for concrete condition; Ψ_{c,V} = 1.0 for cracked concrete, Ψ_{c,V} = 1.4 for noncracked concrete
 – modification factor for anchors located in a concrete member where h_{a} < 1.5 c_{a1}
 – modification factor for anchors loaded at an angle 90° − α_{V} with the concrete edge; in ACI 31814 – 17.5.2.1 are only discrete values, equation is taken from FIB bulletin 58 – Design of anchorages in concrete (2011)
 h_{a} – height of a failure surface on the concrete side
 l_{e} = h_{ef} ≤ 8 d_{a} – loadbearing length of the anchor in shear
 d_{a} – anchor diameter
 f'_{c} – concrete compressive strength
 c_{a1} – edge distance in the direction of load; according to Cl. 17.5.2.4, for a narrow member, c_{2,max} < 1.5 c_{1} that is also deemed to be thin, h_{a} < 1.5 c_{1}, c'_{1} is used in previous equations instead of c_{1}; the reduced c'_{1} = max (c_{2,max} / 1.5, h_{a} / 1.5, s_{c,max} / 3)
 c_{a2} – edge distance in the direction perpendicular to load
 c_{2,max} – largest edge distance in the direction perpendicular to load
 s_{c,max} – maximum spacing perpendicular to direction of shear, between anchors within a group
If c_{a2} ≤ 1.5 c_{a1} and h_{a} ≤ 1.5 c_{a1}, , where s is the maximum spacing perpendicular to direction of shear, between anchors within a group.
According to ACI 31814 – 175.2.9, where anchor reinforcement is developed in accordance with ACI 31814 – 25 on both sides of the breakout surface, the anchor reinforcement is presumed to transfer the shear forces and concrete breakout strength is not evaluated.
5.7.7 Concrete pryout strength of anchor in shear
Concrete pryout strength is designed according to ACI 31814 – 17.5.3.
ϕV_{cp} = ϕk_{cp} N_{cp}
where:
 ϕ = 0.65 – strength reduction factor for anchors in shear according to ACI 31814 – 17.3.3, editable in Code setup
 k_{cp} = 1.0 for h^{ef} < 2.5 in., k_{cp} = 2.0 for h_{ef} ≥ 2.5 in
 N_{cp} = N_{cb} (concrete breakout strength – all anchors are assumed in tension) in case of castin anchors
According to ACI 31814 – 17.4.2.9, where anchor reinforcement is developed in accordance with ACI 31814 – 25 on both sides of the breakout surface, the anchor reinforcement is presumed to transfer the tension forces and concrete breakout strength is not evaluated.
5.7.8 Interaction of tensile and shear forces
Interaction of tensile and shear forces is assessed according to ACI 31814 – R17.6.
where:
 N_{ua} and V_{ua} – design forces acting on an anchor
 N_{n} and V_{n} – the lowest design strengths determined from all appropriate failure modes
 ς = 5 / 3
5.7.9 Anchors with standoff
The bar element is designed according to AISC 36016. Interaction of shear force is neglected because the minimum length of the anchor to fit the nut under the base plate ensures that the anchor fails in bending before the shear force reaches half the shear resistance and the shear interaction is negligible (up to 7 %). Interaction of bending moment and compressive or tensile force is conservatively assumed as linear. Second order effects are not taken into account.
Shear resistance (AISC 36016 – G):
(ASD)
(LRFD)
 A_{V} = 0.844 ∙ A_{s} – the shear area
 A_{s} – bolt area reduced by threads
 F_{y} – bolt yield strength
 Ω_{V} – safety factor, recommended value is 2
 ϕ_{V} – resistance factor, recommended value is 0.75
Tensile resistance (AISC 36016 – D2):
(ASD)
(LRFD)
 Ω_{t} – safety factor, recommended value is 2
 ϕ_{t} – resistance factor, recommended value is 0.75
Compressive resistance (AISC 36016 – E3)
(ASD)
(LRFD)
 for , for – critical stress
 – elastic buckling stress
 L_{c} = 2 ∙ l – buckling length
 l – length of the bolt element equal to half the base plate thickness + gap + half the bolt diameter
 – radius of gyration of the anchor bolt
 – moment of inertia of the bolt
 Ω_{c} – safety factor, recommended value is 2
 ϕ_{c} – resistance factor, recommended value is 0.75
Bending resistance (AISC 36016 – F11):
(ASD)
(ASD)
 – plastic section modulus of the bolt
 – elastic section modulus of the bolt
 Ω_{c} – safety factor, recommended value is 2
 ϕ_{c} – resistance factor, recommended value is 0.75
Linear interaction:
 N – the tensile (positive) or compressive (negative sign) factored force
 P_{n} – the tensile (positive) or compressive (negative sign) design or allowable strength
 M – the factored bending moment
 M_{n} – the design or allowable bending resistance
5.8 Member capacity design
Member capacity design is performed according to AISC 34110
M_{pe} = 1.1 R_{y} F_{y} Z_{x}
where:
 M_{pe} – the expected moment at the plastic hinge
 R_{y} – ratio of the expected yield stress to the specified minimum yield (Table A3.1)
 F_{y} – yield strength
 Z_{x} – the plastic section modulus
5.9 Detailing
The minimum spacing between bolts and distance to the bolt centre to an edge of a connected part are checked. The minimum spacing 2.66 times (editable in Code setup) the nominal bolt diameter between centres of bolts is checked according to AISC 36016 – J.3.3. The minimum distance to the bolt centre to an edge of a connected part is checked according to AISC 36016 – J.3.4; the values are in Table J3.4 and J3.4M.
The minimal and maximal weld size and the sufficient length of the weld are checked.
The maximal weld size is checked according to AISC 36016 – J2.2b:
 For thinner plate thickness up to 3/16 in the weld size should be no bigger than plate thickness.
 For thinner plate thickness higher than 3/16 in and smaller than 1/4 in the weld size should be no bigger than 3/16 in.
 For thinner plate thickness higher than 1/4 in the weld size should be no bigger than 1/4−1/16 in.
The minimal weld size is checked according to Table J2.4:
 For thinner plate thickness to 1/4 in the weld size should be higher than or equal to 1/8 in.
 For thinner plate thickness over 1/4 in to 1/2 in the weld size should be higher than or equal to 3/16 in.
 For thinner plate thickness over 1/2 in to 3/4 in the weld size should be higher than or equal to 1/4 in.
 For thinner plate thickness over 3/4 in the weld size should be higher than or equal to 5/16 in.
The minimum length of fillet welds should not be less than four times the weld size according to J2.2b (c).
The spacing between anchors should be greater than 4 times anchor diameter according to ACI 31814 – 17.7.1.
5.10 Joint classification
Joints are classified according to joint stiffness to:
 Rigid – joints with insignificant change of original angles between members,
 Semirigid – joints which are assumed to have the capacity to furnish a dependable and known degree of flexural restraint,
 Simple – joints which do not develop bending moments.
Joints are classified according to the commentary in AISC 36016, Cl. B3.4.
 Rigid –
 Semirigid –
 Simple –
where:
 S_{j,ini} – initial stiffness of the joint; the joint stiffness is assumed linear up to the 2/3 of M_{j,Rd}
 L_{b} – theoretical length of the analyzed member
 E – Young's modulus of elasticity
 I_{b} – moment of inertia of the analyzed member
 M_{j,Rd} – joint design moment resistance
5.11 Capacity design
The objective of capacity design is to confirm a building undergoes controlled ductile behaviour in order to avoid collapse in a designlevel earthquake. Plastic hinge is expected to appear in dissipative item and all nondissipative items of the joint must be able to safely transfer forces due to the yielding in the dissipative item. The dissipative item is usually a beam in moment resisting frame but it may also be e.g. an end plate. The safety (resistance) factor is not used for dissipative items. Two factors are assigned to the dissipative item:
 R_{y} – overstrength factor; editable in materials
 – strainhardening factor – AISC 35816 (2.42); it is recommended to apply for beam as a dissipative item in moment resisting frame
The material diagram is modified according to the following figure:
The increased strength of the dissipative item allows for the input of loads that cause the plastic hinge to appear in the dissipative item. In the case of moment resisting frame and beam as the dissipative item, the beam should be loaded by M_{y} = C_{pr}R_{y}F_{y}W_{pl,y} and corresponding shear forceV_{z} = –2 M_{y,Ed} / L_{h}, where:
 F_{y} – yield strength
 W_{pl,y} – plastic section modulus
 L_{h} – distance between plastic hinges on the beam
In case of asymmetric joint, the beam should be loaded by both sagging and hogging bending moments and their corresponding shear forces.
The plates of dissipative items are excluded from check.