   # Draw the influence lines for the vertical reactions at support A and C and the shear and bending moment at point B of the beam shown in Fig. P8.6. FIG. P8.6, P8.61

#### Solutions

Chapter
Section
Chapter 8, Problem 6P
Textbook Problem
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## Draw the influence lines for the vertical reactions at support A and C and the shear and bending moment at point B of the beam shown in Fig. P8.6. FIG. P8.6, P8.61

To determine

Draw the influence lines for the vertical reactions at supports A and C.

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

### Explanation of Solution

Calculation:

Apply a 1 kN unit moving load at a distance of x from left end A.

Sketch the free body diagram of beam as shown in Figure 1.

Refer Figure 1.

Find the equation of support reaction (Cy) at C using equilibrium equation:

Consider moment equilibrium at point A.

Consider clockwise moment as positive and anticlockwise moment as negative

Sum of moment at point A is zero.

ΣMA=0Cy(14)1(x)=014Cy=xCy=x14 (1)

Find the equation of support reaction (Ay) at A using equilibrium equation:

Apply vertical equilibrium equation of forces.

Consider upward force as positive (+) and downward force as negative ().

Ay+Cy=1

Substitute x14 for Cy.

Ay+x14=1Ay=1x14 (2)

Consider Equation (2).

Find the value of influence line ordinate of reaction Ay at support A.

Substitute 0 for x in Equation (2).

Ay=1014=1kN/kN

Similarly calculate the influence line ordinate of reaction Ay for different value of x and summarize the result in Table 1.

 x (m) Ay (kN/kN) 0 1 14 0 18 −27

Draw the influence line diagram for the vertical reactions at support A using Table 1 as shown in Figure 2.

Consider Equation (1).

Find the influence line ordinate of reaction Cy at support C.

Substitute 0 for x in Equation (1).

Cy=014=0

Similarly calculate the influence line ordinate of reaction Cy for different value of x and summarize the result in Table 2.

 x (m) Cy (kN/kN) 0 0 14 1 18 97

Draw the influence line diagram for the vertical reactions at support C using Table 2 as shown in Figure 3.

Find the equation of shear force at B of portion AB (0x<7m).

Sketch the free body diagram of the section AB as shown in Figure 4.

Refer Figure 4.

Apply equilibrium equation of forces.

Consider upward force as positive (+) and downward force as negative ().

ΣFy=0

AySB1=0SB=Ay1

Substitute 1x14 for Ay.

SB=(1x14)1=x14

Find the equation of shear force at B of portion BD (7m<x18m).

Sketch the free body diagram of the section BD as shown in Figure 5.

Refer Figure 5.

Apply equilibrium equation of forces.

Consider upward force as positive (+) and downward force as negative ()

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