   # Draw the influence lines for the shear and bending moment at point B of the beam shown in Fig. P8.13. FIG. P8.13, P8.14, P8.15

#### Solutions

Chapter
Section
Chapter 8, Problem 14P
Textbook Problem
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## Draw the influence lines for the shear and bending moment at point B of the beam shown in Fig. P8.13. FIG. P8.13, P8.14, P8.15

To determine

Draw the influence lines for the shear and bending moment at point B.

### Explanation of Solution

Calculation:

Use Muller-Breslau's principle.

Cut the beam at D to obtain the released structure of the beam. Next apply a small relative displacement in positive direction of SB by moving end B of the portion AB downward by Δ2 and end C of the portion BE upward by Δ1 to obtain the deflected shape.

Sketch the deflected shape of the released structure when cut the beam at B as shown in Figure 1.

The general shape of the influence line for shear (SB) at B is the similar of deflected shape.

Sketch the general shape of the influence line for shear (SB) at B as shown in Figure 2.

Find the numerical value of influence line ordinate at B.

Place the 1 k load first just to the left of B and then just to the right of B.

Sketch the free body diagram of beam as shown in Figure 3.

Refer Figure 3.

Find the vertical reaction (Ay) at A.

Take moment at C.

Consider clockwise moment as positive and anticlockwise moment as negative

ΣMC=0(Ay×12)(1×6)=0Ay=12kN

Find the vertical reaction (Ey) at E.

Consider force equilibrium equation.

Consider the vertical forces equilibrium condition, take the upward force as positive (+) and downward force as negative ().

ΣFy=0Ay1+Ey=0

Substitute 12kN for Ay.

121+Ey=0Ey=12kN

Find the shear at B(SB,L) when unit load 1 k placed just left of B using the equation:

SB,L=Ey

Substitute 12kN for Ey

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