The beam is made of an elastic-plastic material for which σY = 200 MPa. If the largest moment in the beam occurs within the center section a-a, determine the magnitude of each force P that causes this moment to be (a) the largest elastic moment and (b) the largest plastic moment.

Question

The beam is made of an elastic-plastic material for which [latex]{ \sigma }_{ Y }[/latex] = 200 MPa. If the largest moment in the beam occurs within the center section a-a, determine the magnitude of each force P that causes this moment to be (a) the largest elastic moment and (b) the largest plastic moment.

Accepted Answer

M = 2P (1)

a) Elastic moment

[latex] I=\frac{1}{12}(0.1)\left(0.2^{3}\right)=66.667\left(10^{-6}\right) m ^{4} [/latex]

[latex] \sigma_{Y}=\frac{M_{Y} C}{I} [/latex]

[latex] M_{Y}=\frac{200\left(10^{6}\right) (66.667)\left(10^{-6}\right)}{0.1} [/latex]

= 133.33 kN • m

From Eq. (1)

133.33 = 2 P

P = 66.7 kN

b) Plastic moment

[latex] M_{p}=\frac{b h^{2}}{4} \sigma_{Y} [/latex]

[latex] =\frac{0.1\left(0.2^{2}\right)}{4}(200)\left(10^{6}\right) [/latex]

= 200 kN • m

From Eq. (1)

200 = 2 P

P = 100 kN

Question : The beam is made of an elastic-plastic material for which σY...

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