   # Draw the influence line for the vertical deflection at point D of the beam of Problem 8.6. EI = constant. See Fig. P8.6. FIG. P8.6, P8.61

#### Solutions

Chapter
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Chapter 8, Problem 61P
Textbook Problem
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## Draw the influence line for the vertical deflection at point D of the beam of Problem 8.6. EI = constant. See Fig. P8.6. FIG. P8.6, P8.61

To determine

Sketch the influence line for the vertical deflection at the point D of the beam.

### Explanation of Solution

Given information:

Calculation:

Consider a unit point load is acting at a distance x from the left support.

Show the loading on the simply supported beam as shown in Figure 1.

Refer Figure 1.

Consider the beam portion ranges from 0mx14m support A.

Show the expression for the deflection of the beam between the supports of overhanging beam due to point load P acting at a distance a from the left support as follows:

Δ=Pax6lEI(l2x2),0<x<l        (1)

Here, l is the length of the beam between the supports and a is the length of the overhanging portion of the beam.

Calculate the deflection (fBX) of the simply supported beam at point D due to the unit point load acting at a distance x from the left support.

Substitute 1 for P, 18m for l, and 4m for a in Equation (1).

Δ=4x6×14EI(142x2)=121EI(196xx3)        (2)

Consider the load is acting at a distance x as 2m.

Calculate the deflection at D as follows:

Substitute 2m for x in Equation (2).

fBX=121EI(196×223)=18.285EI

Similarly, calculate the deflection at point B due to different position of the point load and tabulate the values as shown in Table 1.

 x (m) fBX 2 18.285EI 4 34.285EI 8 50.285EI 12 29.714EI 14 0

Consider the beam portion ranges from 0mx4m(FromsupportC)

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