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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 9, Problem 21P
Textbook Problem
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Determine the absolute maximum bending moment in a 75 ft long simply supported beam due to the wheel loads of the moving HS15-44 truck shown in Fig. P9.15.

Chapter 9, Problem 21P, Determine the absolute maximum bending moment in a 75 ft long simply supported beam due to the wheel

FIG. P9.15, P9.21

To determine

Find the absolute maximum bending moment in a 75 ft long simply supported beam.

Explanation of Solution

Calculation:

Sketch the simply supported beam as shown in Figure 1.

Sketch the loading position and resultant as shown in Figure 2.

Refer Figure 2.

Find the resultant load (PR).

PR=12+12+3=27k

Find the location of the resultant (x¯).

Consider moment of the resultant about a point equals the sum of the moments of the individual loads about the same point.

Take moment at load 1.

PR(x¯)=12(20)+3(34)PR(x¯)=342

Substitute 27 k for PR.

(27)x¯=342x¯=12.67ft

Find the position of loads on the beam.

As per the observation, the resultant is closest to the second load. Hence, the maximum bending moment occurs under the second load. The series of the load is positioned on the beam so that the midspan of the beam is located halfway between the load 2 and the resultant.

Find the distance between the resultant and second load.

x2=20x¯

Substitute 12.67ft for x¯.

x2=2012.67=7.33ft

Find the position of second load and resultant from center of the beam.

Location of resultant=x22

Substitute 7.33 ft for x2

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