Fire design: T-stub
Analytical Model
Only tension loads are considered in this study. Effective lengths for circular and noncircular failures are considered according to EN 1993-1-8:2005, Cl. 6.2.6. Three modes of collapse according to EN 1993-1-8:2005, Cl. 6.2.4.1 are considered: 1. mode with full yielding of the flange, 2. mode with two yield lines by web and rupture of the bolts, and 3. mode for rupture of the bolts; see Fig. 1. Bolts are designed according to Cl. 3.6.1 in EN 1993-1-8:2005.
Fig. 1: Failure modes of T-stub in tension
The tension strength of bolted T-stubs failed by flange yielding at elevated temperatures could be calculated as
\[F_{T,1,Rd,\theta}=\frac{4M_{pl,1,Rd,\theta}}{m}\]
\[M_{pl,1,Rd,\theta}=0.25 \Sigma l_{eff,1} t_f^2 f_{y,\theta} / \gamma_{M,fi} \]
where \(\gamma_{M,fi}=1.0\) is the partial factor provided by Eurocode, \(f_{y,\theta}\) is the yield strength of T-stub flange at elevated temperature θ, \(M_{pl,1,Rd,\theta}\) is the bending strength of T-stub flange at elevated temperature θ, \(l_{eff}\) is the total length of the yielding line of the T-stub.
Eurocode 3-1-8 provides equations to calculate the tension strength of the bolted T-stub fails by flange yielding accompanied with bolt failure at ambient temperatures.
\[F_{T,2,Rd,\theta}=\frac{2M_{pl,2,Rd,\theta}+e \Sigma F_{T,Rd,\theta}}{m+e}\]
\[M_{pl,2,Rd,\theta}=0.25 \Sigma l_{eff,2} t_f^2 f_{y,\theta} / \gamma_{M,fi}\]
\[F_{T,Rd,\theta}=\frac{k_2 f_{ub,\theta} A_s}{\gamma_{M,fi}}\]
where e is the distance between axis of bolt hole and edge of T-stub flange, \(l_{eff,2}\) is the total length of the yielding line of T-stubs, \(f_{ub,\theta}\) is the ultimate tensile strength of bolt at elevated temperature θ, \(l_{eff,2}\) is the total length of the yielding line of the T-stub, \(M_{pl,2,Rd,\theta}\) is the bending strength of T-stub flange at elevated temperature θ, \(A_s\) is the effective cross-section area of a bolt, \(\gamma_{M,fi}=1.0\) is the partial safety factor.
l_(eff,1,2)=min(l_(eff,cp),l_(eff,np),l_(eff,bp))
l_(eff,cp)=2πm circular pattern
l_(eff,np)=4m+1.25n non-circular pattern
l_(eff,bp)=b beam pattern
The tension strength of bolt failure at elevated temperatures could be calculated by
F_(T,3,Rd,θ)=∑▒F_(T,Rd,θ)
where F_(T,Rd,θ) is the tension resistance of bolts at temperature θ.
Verification
Benchmark example
Inputs
T-stub, see Fig. 5.1.11
- Steel S235
- Flange thickness tf = 20 mm
- Web thickness tw = 20 mm
- Flange width bf = 300 mm
- Length b = 100 mm
- Double fillet weld aw = 10 mm
Bolts
- 2 × M24 8.8
- Distance of the bolts w = 165 mm
Code setup – Model and mesh
- Number of elements on biggest member or flange 16
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