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9th Edition

Barry J. Goodno + 1 other

Publisher: Cengage Learning

ISBN: 9781337093347

Chapter 4, Problem 4.5.29P

Textbook Problem

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A beam of length *L *is designed to support a uniform load of intensity *q *(see figure). If the supports of the beam are placed at the ends, creating a simple beam, the maximum bending moment in the beam is *qL ^{2}/8. *However, if the supports of the beam are moved symmetrically toward the middle of the beam (as shown), the maximum bending moment is reduced.

- Determine the distance
*a*between the supports so that the maximum bending moment in the beam has the smallest possible numerical value. Draw the shear-force and bending-moment diagrams for this condition. - Repeat part (a) if the uniform load is replaced with a triangularly distributed load with peak intensity
*q*=_{0}*q*at mid-span (see Fig. b).

a.

To determine

The distance a between the support by having the small numerical value of maximum bending moment and to draw the diagrams of shear force and bending moment.

**Given:**

The given figure

The length of the beam L supports the load which is uniform having the intensity as q. The bending moment that is maximum is given as

**Concept Used:**

Resultant force,

**Calculation:**

As the forces are symmetry,

At a distance from x to C, the section between CA is considered,

When x=0,

When

At a distance from x to C, the section between AB is considered,

When

When,

b.

To determine

The distance ‘a’ between the support by having the small numerical value of maximum bending moment and to draw the diagrams of shear force and bending moment.

Mechanics of Materials (MindTap Course List)

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