Question

Which of the following relation is correct for pin based frames?

(a) Mp =γL(wL^2/8)[1-k+(1+k)^0.5].

(b) Mp =γL(wL^2/8)[1+k+(1-k)^0.5].

(c) Mp =γL(wL^2/8)[1+k-(1+k)^0.5].

(d) Mp =γL(wL^2/8)[1+k+(1+k)^0.5].

I got this question in exam.

My question is based upon Plastic Design of Portal Frames, Effect of Axial and Shear force on Plastic Moment Capacity topic in chapter Plastic and Local Buckling Behaviour of Steel of Design of Steel Structures

Answer 1

Correct option is (d) Mp =γL(wL^2/8)[1+k+(1+k)^0.5].

Easiest explanation: When gravity load governs the design, a good estimate of required section may be obtained by using following formulae :

For pin based frames : Mp =γL(wL^2/8)[1+k+(1+k)^0.5]

For fixed=-base frame : Mp =γL(wL^2/8)[1/[1+0.5k+(1+k)^0.5]], where γL = 1.7 global load factor, k = h2/h1.