A rectangular steel bar, with 8" x 0.75" cross-sectional dimensions, has equal and opposite moments applied to its ends.

a. Determine the yield moment assuming Fy = 50 ksi.
b. For the moment calculated in part a, calculate the strain in the cross-section 2 inches down from the top of the rectangle.
c. Determine the plastic moment assuming Fy = 50 ksi.

Part a: The yield moment is 400 k.in.

Part b: The strain is

Part c: The plastic moment is 600 ksi.

Explanation:

Part a:

As per bending equation

Here

Here

The yield moment is 400 k.in.

Part b:

The strain is given as

The stress at the station 2" down from the top is estimated by ratio of triangles as

Now the steel has the elastic modulus of E=29000 ksi

So the strain is

Part c:

For a rectangular shape the shape factor is given as 1.5.

Now the plastic moment is given as

The plastic moment is 600 ksi.

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explanation: