Solving for F kip 588 and 994 are incorrect A steel bar of t

Solving for F (kip). 5.88 and 9.94 are incorrect.

A steel bar of thickness h is subjected to a bending force F. The vertical support is stepped such that the horizontal welds are b_1 and b_2 long. Determine F if the maximum allowable weld shear stress is tau_allow.

Solution

In this section due to eccentricity of loading, joint fails in shear along throat section. For given loading , throat area subjected to 2 types of shear stress

Direct shear of magnitude (F/2lt)

‘l=Length of weld

‘t= Thickness @ throat

Indirect shear stress owing to eccentricity of loading. Shear stress is proportional to its distance from centroid of throat area. i.e.

‘ (r) = c x r

C = Proportionality constant

Tanking Moment about centroid

L= Distance of line of action of F from centroid

C= F x (b₂+c)/j

Taking moment about centroid

Ø x (r) x r x dA = F x L