   # Draw the influence lines for the shear and bending moment point C of the beam shown in Fig. P8.27. FIG. P8.27, P8.28

#### Solutions

Chapter
Section
Chapter 8, Problem 28P
Textbook Problem
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## Draw the influence lines for the shear and bending moment point C of the beam shown in Fig. P8.27. FIG. P8.27, P8.28

To determine

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

### Explanation of Solution

Calculation:

Use Muller-Breslau's principle.

Cut the beam at C to obtain the released structure of the beam. Next apply a small relative displacement in positive direction of SC by moving end C of the portion BC downward by Δ1 and end C of the portion CD upward by Δ2 to obtain the deflected shape.

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

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

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

Find the numerical value of influence line ordinate of SC at C.

Place the 1 kN load first just to the left of F and then just to the right of F.

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

Find the vertical reaction (Ay) at A.

Find the vertical reaction (Fy) at F.

Consider moment at E from G.

Consider clockwise moment as negative and anticlockwise moment as positive.

ΣME=0Fy(4)=0Fy=0

Consider moment at B from G.

Consider clockwise moment as negative and anticlockwise moment as positive.

ΣMB=0Fy(11)+Dy(6)1(3)=00(11)+6Dy3=0Dy=12kN

Find the vertical reactions Ay.

Apply force equilibrium equation.

Consider upward force as positive and downward force as negative.

Ay+Dy+Fy=1

Substitute 12kN for Dy and 0 for Fy.

Ay+Dy+Fy=1Ay+12+0=1Ay=12kN

Find the shear at C(SC,L) when unit load 1 kN placed just left of C using the equation:

SC,L=Dy

Substitute 12k for Dy.

SC,L=12kN

Thus, the value of influence line ordinate just left of C is 12kN/kN.

Find the shear at F(SC,R) when unit load 1 k placed just right of C using the equation:

SC,R=Ay

Substitute 12kN/kN for Ay

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