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Structural Analysis

6th Edition
KASSIMALI + 1 other
Publisher: Cengage,
ISBN: 9781337630931

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Section
BuyFindarrow_forward

Structural Analysis

6th Edition
KASSIMALI + 1 other
Publisher: Cengage,
ISBN: 9781337630931
Chapter 8, Problem 58P
Textbook Problem
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Draw the influence line for the vertical deflection at point B of the cantilever beam of Problem 8.5. EI = constant. See Fig. P8.5.

Chapter 8, Problem 58P, Draw the influence line for the vertical deflection at point B of the cantilever beam of Problem

FIG. P8.5, P8.58

To determine

Sketch the influence line for the vertical deflection at the point B of the given cantilever beam.

Explanation of Solution

Given information:

Calculation:

Consider a point load is acting at a distance x from the fixed end of the given cantilever beam.

Show the loading on the cantilever beam as shown in Figure 1.

Refer Figure 1.

Consider the beam portion ranges from 0ftx24ft.

Show the expression for the deflection of the cantilever beam due to point load P acting at a distance a from the fixed end as follows:

Δ=Px26EI(3ax),0<x<a        (1)

Here, E is modulus of elasticity of the beam, I is the moment of inertia.

Calculate the deflection (fBX) of the cantilever beam at point B due to the unit point load acting at a distance x from the fixed end.

Substitute 1 for P and 24ft for a in Equation (1).

fBX=x26EI(3×24x)fBX=16EI(72x2x3)fBX=16EI(x372x2)        (2)

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

Calculate the deflection at B as follows:

Substitute 2ft for x in Equation (2).

fBX=16EI(2372×22)fBX=46.66EI

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 (ft)fBX
246.66EI
6396EI
101033.33EI
141894

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Chapter 8 Solutions

Structural Analysis
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