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9th Edition

Barry J. Goodno + 1 other

Publisher: Cengage Learning

ISBN: 9781337093347

Chapter 5, Problem 5.5.17P

Textbook Problem

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A simple beam *A B *of a span length *L = *24 ft is subjected to two wheel loads acting at a distance *d = 5 *ft apart (see figure). Each wheel transmits a load *P = *3.0 kips, and the carriage may occupy any position on the beam.

- Determine the maximum bending stress G
_{m}_{a}_{x}_{}due to the wheel loads if the beam is an I-beam having section modulus*S =*16.2 in^{3}. - If
*d = 5*ft. Find the required span length*L*to reduce the maximum stress in part (a) to 18 ksi. - If L = 24 ft, Find the required wheel spacing
*s*to reduce the maximum stress in part (a) to 18 ksi.

a.

To determine

The maximum bending stress due to wheel loads.

**Given:**

Length of beam, L = 24ft = 288 in. Distance between the wheel, d = 5ft = 60 in, Section modulus, S = 16.2 in., point load transmitted through one wheel, P = 3kip.

**Concept Used:**

The problem is carried out by using pure bending equation. When bending stress is developed along the axis of the material, the stress and strain can be calculated based on this equation

E = young’s modulus, R = radius of gyration, M = Bending moment, I = moment of inertia,

**Calculation:**

Reaction a A

Moment using Reaction at A,

b.

To determine

The length required if the maximum stress is 18ksi

c.

To determine

The wheel spacing‘d’ for 18kip stress provided L = 24ft

Mechanics of Materials (MindTap Course List)

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