Mechanics of Materials
Mechanics of Materials
9th Edition
ISBN: 9780133254426
Author: Russell C. Hibbeler
Publisher: Prentice Hall
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Chapter 11.4, Problem 11.33P
To determine

Find the absolute maximum normal stress in the beam and specify its location.

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We will consider a linear system and a nonlinear system under uncertainty, each expressed in the form of a set of stochastic differential equation (SDE) as follows: = da (Ax+ Bu)dt + Gdw, dx = f(x,u,t)dt+Gdw, (1) (2) where x is the state, u is the control, and dw is a differential increment of standard Brownian motion, i.e., E[dw] = 0 and E [dw(t)dw(t)] = dt-1. In this problem, we consider the linear SDE, Eq. (1), with a very simple model where x = R², u = [0,0] (no control), and dw R². The matrices A, B, and G are given as follows: A=02x2, B=02x2; G = [000] (3) where σp Є R represents the degree of the uncertainty, and let us take σ₁ = 2 and σ2 = 3. Assume that the initial state is deterministic and e(t = 0) = [0,0]. Take the following steps to simulate the given SDE for 1 € [0, 1]: (a): Consider the increments of w between each time interval [+1). Derive the analytical expression of Aw using w~N(02, 12), where Aw, w(tk+1) — w(tk). (c): Derive the approximate continuous-time EoM from…

Chapter 11 Solutions

Mechanics of Materials

Ch. 11.2 - The allowable bending stress is allow = 24 ksi and...Ch. 11.2 - The allowable bending stress is allow = 22 ksi and...Ch. 11.2 - 11–7. Draw the shear and moment diagrams for the...Ch. 11.2 - *11–8. The simply supported beam is made of timber...Ch. 11.2 - The beam has an allowable normal stress of allow =...Ch. 11.2 - The beam has an allowable normal stress of allow...Ch. 11.2 - 11–11. The timber beam is to be loaded as shown....Ch. 11.2 - If each beam is to be designed to carry 90 lb/ft...Ch. 11.2 - 11–13. Select the lightest steel wide-flange beam...Ch. 11.2 - 11–14. Select the lightest-weight steel...Ch. 11.2 - Prob. 11.15PCh. 11.2 - The beam has an allowable normal stress of allow....Ch. 11.2 - Determine the maximum cable force P that can...Ch. 11.2 - to safely support the load. The wood has an...Ch. 11.2 - and the wood has an allowable normal stress of...Ch. 11.2 - Prob. 11.20PCh. 11.2 - Prob. 11.21PCh. 11.2 - Prob. 11.22PCh. 11.2 - 11–23. The beam is constructed from three boards...Ch. 11.2 - Prob. 11.24PCh. 11.2 - Prob. 11.25PCh. 11.2 - Select the lightest-weight wide-flange beam from...Ch. 11.2 - Prob. 11.27PCh. 11.2 - * 11–28. The joist AB used in housing construction...Ch. 11.2 - If the maximum bending stress is not to exceed...Ch. 11.2 - 11–30. The simply supported beam supports a load...Ch. 11.4 - Determine the variation in the width was a...Ch. 11.4 - Prob. 11.32PCh. 11.4 - Prob. 11.33PCh. 11.4 - The beam is made from a plate that has a constant...Ch. 11.4 - Determine the variation in the depth d of a...Ch. 11.4 - Determine the variation of the radius r of the...Ch. 11.4 - Prob. 11.37PCh. 11.4 - Determine the variation in the width b as a...Ch. 11.4 - The tubular shaft has an inner diameter of 15 mm....Ch. 11.4 - Prob. 11.40PCh. 11.4 - Prob. 11.41PCh. 11.4 - Prob. 11.42PCh. 11.4 - Prob. 11.43PCh. 11.4 - Prob. 11.44PCh. 11.4 - Prob. 11.45PCh. 11.4 - Prob. 11.46PCh. 11 - The cantilevered beam has a circular cross...Ch. 11 - Select the lightest-weight wide-flange overhanging...Ch. 11 - Prob. 11.49RPCh. 11 - Determine the shaft's diameter to the nearest...Ch. 11 - Select the lightest-weight wide-flange beam from...Ch. 11 - The simply supported joist is used in the...Ch. 11 - The simply supported joist is used in the...Ch. 11 - by 4-in. pieces of wood braced as shown. If the...
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