Problem

Determine the reactions and draw the shear and bending moment diagrams for the beams sho...

Determine the reactions and draw the shear and bending moment diagrams for the beams shown in Figs. PD.1 through PD.8 using the three-moment equation.

Step-by-Step Solution

Solution 1

Step #1 of 13

Draw the free body diagram of the actual beam as follows:

Step #2 of 13

Compute the bending moment at B:

Substitute for and for L.

Step #3 of 13

Equivalent Beam for analysis by three –moment equation:

Step #4 of 13

Apply Three- moment equation at joint A.

…… (1)

Here, is the bending moment at point A, is the modulus of elasticity, are the bending moments at the adjacent supports to the left and to right of C, are the length of spans to the left and right of C, are the concentrated loads are the ratios of the distances of the from the left or right support to the span length, , are the settlements of the adjacent supports to the left and right of C, is the settlement of the support c under consideration and are the moment of inertia of the beam.