A circular solid rod of diameter ‘d’ welded to a rigid flat plate by a circular fillet weld of throat thickness ‘t’ is subjected to a twisting moment ‘T’. The maximum shear stress induced in the weld is

Question

Question

This question was previously asked in

UPPSC AE Mechanical 2019 Official Paper I (Held on 13 Dec 2020)

Answer 1

Explanation:

Welded joint subjected to twisting moment:

We know that the shear stress induced by twisting moment
where,

T = twisting moment, Zp = section modulus of weld section

J_p = Ixx + Iyy = polar moment of inertia of weld section

I_xx, I_yy = moment of inertia along x-x and y-y direction,

d = 2r = diameter of rod

The moment of inertia of annular fillet is obtained by considering a small element of:

δA = area of small section = rdθ × t

δI_xx= y²δA

Integrating the above expression we get the moment of inertia in the x-x plane

Ixx = Iyy = πtr3

J_p = I_xx + I_yy = πtr³ + πtr³ = 2πtr³

Note: Remember the formula of polar moment of inertia (J_p) for a circular filler to save your time in the exam.