Consider the beam (AC) of length L supported by a pin joint at C and a roller at

Question

Consider the beam (AC) of length L supported by a pin joint at C and a roller at A with a downward force P applied at L/2. The beam has a square cross-section of side length a. The beam AC is made of a material of yield stress [sigma]y (both in tension and in compression; assume elasticperfectly plastic behavior).

(i) What is the force P that can be applied to the beam at its mid point (as shown) when the beam just begins to yield (in terms of [sigma]y, a)? Where does yielding begin (sketch the beam and point out the location(s) on the sketch)?

(ii) What is the maximum force P that the beam can support (in terms of [sigma]y, a, L)?

(iii) Where does the plastic hinge form when the beam is supporting the maximum force it can?

Sketch the deformed shape of the beam when a plastic hinge forms.

Explanation / Answer

i hope this can help you : http://www3.esc.auckland.ac.nz/people/staff/pkel015/SolidMechanicsBooks/Part_I/BookSM_Part_I/04_LinearElasticity%20I/PDF/Linear_Elasticity_06_Beam_Theory.pdf

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