   # 8.59 and 8.60 Draw the influence line for the vertical deflection at point B of the simply supported beams of Problems 8.1 and 8.2. EI = constant. See Figs. P8.1 and P8.2. FIG. P8.2, P8.60

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Chapter 8, Problem 60P
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## 8.59 and 8.60 Draw the influence line for the vertical deflection at point B of the simply supported beams of Problems 8.1 and 8.2. EI = constant. See Figs. P8.1 and P8.2. FIG. P8.2, P8.60

To determine

Sketch the influence line for the vertical deflection at the point B of the simply supported beam.

### Explanation of Solution

Given information:

Calculation:

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

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

Refer Figure 1.

Consider the beam portion ranges from 0mx4m.

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

Δ=Pbx6lEI(l2x2b2),0<x<a        (1)

Here, a and b are the location of the point load from the left and right support, and l is the length of the beam.

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

Substitute 1 for P, 16m for l, and 12m for b in Equation (1).

fBX=1×12×x6×16EI(162x2122)fBX=18EI(112xx3)        (2)

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

Calculate the deflection at B as follows:

Substitute 2m for x in Equation (2).

fBX=18EI(112×223)fBX=27EI

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 −27EI 3 −38.625EI 4 −48EI

Consider the beam portion ranges from 4mx16m.

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

Δ=Pb6lEI[lb(xa)3+(l2b2)xx3],a<x<l        (3)

Here, l is the distance between the fixed end and the section where the deflection is required, E is modulus of elasticity of the beam, and I is the moment of inertia.

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

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