# Solved Example: Analysis of a welded steel beam-to-column connection (BS 5950)

Articles > Solved Example: Analysis of a welded steel beam-to-column connection (BS 5950)

### Question:

A grade S275 steel 610 × 229 × 101 UB is to be connected, via a welded end plate onto a 356 × 368 × 177 UC. The connection is to be designed to transmit a bending moment of 500 kN m and a shear force of 300 kN. Show that the proposed welding scheme for this connection is adequate.

### Solution:

Leg length of weld, s = 10 mm. Effective length of weld is

$4(l_w-2s)+2(h_w-2s)=4(225-2*10)+2(570-2*10)=1920mm$

$Weld\;force=\frac{shear\;force}{effective\;length\;of\;weld}=\frac{300}{1920}=0.16kN/mm$

Weld second moment of area, Ixx, is

$I_{xx}=4[1*(l_w-2s)y_1^2+2[1*(h_w-2s)^3/12]] = 4[(205)293.5^2+2[1*(550)^3/12]]=98365812mm^4$

Weld shear (moment) is

$\frac{M_y}{I_{xx}}=\frac{500*10^3*293.5}{98365812}=1.49 kN/mm$

where y = D/2 = 587/2 = 293.5 mm

Vectored force = sqrt(1.492 + 0.162) = 1.50 kN/mm

Since the steel grade is S275 and the electrode strength is 42, the design strength of the weld is 220 N/mm2.

Weld capacity of 10 mm fillet weld, pwc, is

$\rho_{wc}=\alpha \pho_w=0.7*10*220*10^{-3}=1.54kN/mm>1.50kN/mm$

where throat thickness of weld, a = 0.7s = 0.7 × 10 mm

Hence proposed welding scheme is just adequate.