The Section with the Maximum Shape Factor is the

Answer- a. Triangle

In plastic moment analysis, the section with the maximum shape factor is the triangle.

Solution

Let us understand the reason why in plastic moment analysis, the section with the maximum shape factor is the triangle. For structural steel, the members reserve some additional strength after the first yield, i.e, yielding of the extreme fibres due to plastification. The shape factor of a member signifies how much of this reserve strength is available for that member. The shape factor of a section is the ratio of its plastic moment to its yield moment. It depends on the shape of the cross-section of the member and is independent of dimensions.

Shape Factor, S.F = M_P/M_y

Where,

• M_P = plastic moment=f_yZ_P
• and M_y=yield moment=f_yZ_e

S.F = f_yZ_p/f_yZ_e = Z_p/Z_e

Where,

• Z_p=plastic section modulus
• Z_e=elastic section modulus

Example: The shape factor of the rectangular section is 1.5. This indicates that a rectangular section can take 50% more moments than the yield moment till failure.

The shape factor for the different sections is given below:

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