Question

Determine the elastic neutral axis, elastic section modulus, plastic neutral axis and plastic section modulus for a C9x20 section modeled as 3 rectangles (flanges and the web). Compare the calculated values with those given in the manual.

Answer 1

" Since it is slgmmetrical to n axis elastic neutral axis and plastic neutral axis will be same Y^bar = elastic neutral axis Y^bar = 4.5^"" Area of channel: A = 5.8459in^2 I_nn = 2 [2.648 times 0.413^3/12 + (2.648 times 0.413 times 4.294^2)] + 0.448 times 8.174^3/12 = 40.36 + 20.39 I_nn = 60.75 in ^y (I_nn = 60.9 in^4 from table) elastic section modules = I_xx/4^bar = 60.75/4.5 = 13.5 in^3 Elastic section modules = 13.5 in^3 Axis which divide the channel are into 2 equal part is known as plastic neutral axis Y_p^bar = 4.5 "" Plastic section modules, Z_p = A/2 [Y_1 ^bar + Y_2 ^bar] Y_1^bar = Y_2^bar = (4.087 times 0.448 times 2.044) + (2.648 times 0.413 times 4.294)/2.925 Y_1 ^bar = Y_2 ^bar = 2.885inch Z_p = 5.8459/2 [2.885 + 2.885] Z_p = 16.87 inch^3"