Problem 4. Use Singularity Functions to determine the slope and displacement equ

Question

Problem 4. Use Singularity Functions to determine the slope and displacement equations. From these equations, find slopes at A, B, C, D, E, and displacements at C, D and E. Plot the displacement and slope profiles along the member length. Check displacements and slopes at D and E using Virtual Work 2PL P D E L/4 L/2 Problem 5. With Singularity Functions find the slope and displacement equations. Calculate maximum slope and displacement at D using these equations and check with Virtual Work. Plot the displacement and slope profiles along the member length. 15 kips 10 kips/ft 20 ft

Explanation / Answer

1> To find the slopes and deflections in the joints first calculate support reactions and draw bending moment diagram of given beam and divide moment by EI to consider material properties also.(M/EI diagram) .Then convert the beam into conjugate beam by changing the support condiction. Here hinge joint will remain hinge in conjugate beam.

In conjugate beam apply the M/EI diagram as load.

For slope at any point calculate shear force at that point in conjugate beam.

For deflection at any point calculate bending moment at that point in conjugate beam.

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