The plastic modulus of a section is 4.8 × 10 -4 m 3. The shape fa

SOLUTION

Concept:

Shape Factor: It is defined as the ratio of moment carrying capacity of the plastic section over that of the elastic section when the yielding just starts.

\(Shape\;Factor = \frac{{{Z_P}{\sigma _y}}}{{{Z_e}{\sigma _y}}} = \frac{{{M_P}}}{{{M_y}}} = \frac{{{Z_P}}}{{{Z_e}}}\)

Shape factor values for different sections:

Calculation:

Plastic modulus of section ZP = 4.8 × 10-4 m3

Plastic moment Capacity MP = 120 kNm

Plastic moment capacity is given by,

\({M_P} = {Z_P}{\sigma _y}\)

Yield Stress is given by,

\({\sigma _y} = \frac{{{M_P}}}{{{Z_P}}} = \frac{{120 \times 1000}}{{4.8 \times {{10}^{ - 4}}}} = 250 \times {10^6}\;N/{m^2} = 250\;MPa\)