# What is the maximum deflection and bending moment of a hinged hinged beam? [closed]

It is not a simply supported beam with one end hinged the other end with roller support. I am working on both the ends hinged beam. i.e at the two ends only rotation about z axis is allowed and all other dof are zero. Or constrained in X,Y,Z and about Theta X, Theta Y and free to rotate about Theta Z only. Point load is applied at the center of the hinged hinged beam.

• Could you please post a sketch? Jun 3 '18 at 12:38
– Wasabi
Jun 4 '18 at 16:56
• It is not possible to answer the question like that. From a statical point of view the reaction forces and bending moments are equal to the ones you'd get if one end was hinged and the other one with roller support. The problem is that a two-hinge beam is statically indeterminate. This leads to residual stresses, say for example through thermal expansion/contraction, because it gets forced to a certain length. Jun 5 '18 at 5:54

I assumed by hinged beam you mean pin and roller support. Otherwise it would be an indeterminate structure. Because we would need to consider the effect of longitudinal strain, like a suspended cable bridge and normal bending.

If we consider a simply supported beam:

$$M_{max} = pl/4$$ $$\delta_{max} = pl^3/{48EI}$$