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6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 9, Problem 5P

Textbook Problem

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For the cantilever beam of Problem 8.5, determine the maximum upward vertical reaction and the maximum counterclockwise reaction moment at support *A* due to a concentrated live load of 25 k, a uniformly distributed live load of 2 k/ft, and a uniformly distributed dead load of 0.5 k/ft.

FIG. P8.5, P8.58

To determine

Find the maximum upward vertical reaction and the maximum counterclockwise reaction moment at support *A*.

**Given Information:**

The concentrated live load (*P)* is 25 k.

The uniformly distributed live load

The uniformly distributed dead load

**Calculation:**

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

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

Refer Figure 1.

**Find the equation of support reaction** ** at A using equilibrium equation:**

Consider upward force as positive

The value of influence line ordinate of reaction is 1 k/k applied throughout the length of the beam.

Draw the influence line diagram for the vertical reaction at support *A* as shown in Figure 2.

Refer Figure 1.

The maximum influence line ordinate due to upward reaction at *A* is 1 k/k.

Find the area of the influence line diagram (*A*) for the vertical reaction at support *A*.

Here, *L* is the length of the beam.

Substitute 36 ft for *L*.

Find the maximum upward vertical reaction at support *A* using the equation.

Substitute 25 k for *P*, 1 k/k for *A*, and 0.5 k/ft for

Therefore, the maximum upward vertical reaction at support *A* is

**Find the equation of reaction moment** ** at support A.**

Take moment about point *A*.

Consider moment equilibrium at point *A*.

Consider clockwise moment as negative and anticlockwise moment as positive.

Sum of moment at point *A* is zero.

Consider Equation (1)

Structural Analysis

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