Question

In elastic stage, equilibrium condition is achieved when neutral axis ___________ and in fully plastic stage, it is achieved when neutral axis ___________

(a) is above centroid of the section, divides the section into two parts of one-third area and two-third area

(b) is below centroid of the section, divides the section into two parts of one-third area and two-third area

(c) is above centroid of the section, divides the section into two equal areas

(d) passes through centroid of the section, divides the section into two equal areas

The question was posed to me in homework.

The above asked question is from Plastic Theory topic in division Plastic and Local Buckling Behaviour of Steel of Design of Steel Structures

Answer 1

The correct answer is (d) passes through centroid of the section, divides the section into two equal areas

To explain: In elastic stage, when bending stress varies from zero at neutral axis  to maximum at extreme fibres, equilibrium condition is achieved when neutral axis passes through centroid of the section. In fully plastic stage, because the stress is uniformly equal to yield stress, equilibrium condition is achieved when neutral axis divides the section into two equal areas.