Maximum bending moment and stress 4

[329moss]

If a central concentrated load is applied mid span of a fixed end beam, then the maximum bending moment occurs at the centre and at the ends of the beam. If at these points moment is greater than the plastic moment, plastic hinges will form. Where will be the maximum stress? Will it be at the points where there are maximum bending moment where the plastic hinges form? Hence the midpoint and at the ends of the beam.

 

[JStephen]

I don't know that there is a good answer. The assumptions used for stress distribution in a beam are either elastic stress Mc/I or uniform stress +/-Fy, and if you get beyond those levels, it seems you'd wind up with a complicated finite element problem. You'd also need a good idea of the stress-strain curve for the particular material in question. You might also have failure by plastic buckling which is not necessarily considered in the normal beam design (that is, you couldn't just assume it didn't happen.)

 

[Lion06]

Once the three hinges form, you have a mechanism and the beam is unstable.

 

[rowingengineer]

Assuming the beam hasn't buckled in local, gobal ect.

How could you do anything so vicious? It was easy my dear, don't forget I spent two years as a building contractor. - Priscilla Presley & Ricardo Montalban

 

[hokie66]

I expect the maximum combined stress would be at the supports, as moment and shear are both maximum there. But why do you ask?

 

[rb1957]

the support plastic hinges mean the supports are (now) working as pinned supports. the central hinge, undr the load, means that the beam is now reacting the load with axial tension.

question, can you apply more shear load onto a section that is fully plastic ? isn't a plastic hinge when the section has fully depended plasticity ? maybe it assumes the section is stressed to +ve and -ve yield stress so there's some room for extra load (or is it +ve and -ve ftu ?)

 

[yakpol]

Moment and stress are equal at support and at midspan, but plastic rotations at midspan are twice as high. Hence midspan section will loose its integrity first.
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