I am looking for the answer to #3. I was able to figure out answer 1 & 2 already

Question

I am looking for the answer to #3. I was able to figure out answer 1 & 2 already.

I am looking for the answer to #3. I already have 1 & 2 done.

1.) A "built-up" section is required elsewhere in this building where a crane will be installed. The owner would like to use a W21x57 vertical beam with at C12x25 flatwise channel above it, as shown in the figure. CI2.x25 a) Find the global or overall centroid of the built-up section (x-axis). b) Find the lx moment of inertia of the built-up member. 2.) Assuming the built-up shape is made of A36 steel (fy 36 ksi), what is the maximum moment capacity of the member (about the x-axis) when the extreme fiber just reaches full yield (its "elastic" bending limit). Additional Homework Question:3.) Find the "weak-axis" moment of inertia (w)of this built-up section, and also its weak-axis "yield moment" capacity limit (point of first yield in the section).

Explanation / Answer

The moment of inertia of the built up section about minor axis will be equal to sum of the moment inertia of w21x57 and c12x25 about the vertical axis.

Moment of inertia of W21x57 about vertical axis will be equal to minor axis moment of w21x57 = 30.6 in4

Moment of inertia of C12x25 about vertical axis will be equal to major axis moment of C12x25 = 144 in4

Iyy = 30.6+144 = 174.6 in4

section modulus of section = 174.6/6 = 29.1 in3

yield stregth of material = 36 ksi

Moment capacity = 36*29.1/12 = 87.3 kip-ft

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