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statically indet beams

# statically indet beams - Statically Indeterminate Beams If...

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Statically Indeterminate Beams If we have too many supports or support conditions a beam will be statically indeterminate and we will not be able to solve for the external reactions or the internal forces. Example: A B L w lb/length A B M B (two equations of equilibrium, three unknown reactions) w

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we can solve statically indeterminate problems if we relate the loads to the deformation In a beam the vertical deflection of the beam, v(x), is related to the internal bending moment, M(x), in the beam, through the relation v(x) ( 29 2 2 d v EI M x dx = E … Young's modulus of the beam (a material property) I … an area moment of the beam cross sectional Area, A ( a geometry property) 2 A I y dA = x y
We can use this relationship and appropriate boundary conditions on the beam slope or vertical deflection to find all the reactions and make the problem solvable. pin or roller support v =0 (no deflection) dv/dx = slope is not constrained fixed (clamped) support v=0 (no deflection) dv/dx =0 (no slope)

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A B L w lb/length Consider our previous example A V(x) M(x) x y x wx x/2 M(x) = Ax –wx 2 /2
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statically indet beams - Statically Indeterminate Beams If...

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