Question 5 A fixed-end beam AB of length L supports a uniform load of intensity q as shown in Figure Q5 Beginning with the second-order differental equation of the deflection curve (the bending moment equation) (5 1) determine the reactions, shear forces, bending moments, slopes, and deflections of the beam construct the shear-force and bending-moment diagrams, labelling all critical ordinates (5 2) Mg Mv Rs L RA Figure Q5 Fixed-end beam

Question 5 A fixed-end beam AB of length L supports a uniform load of intensity q as shown in Figure Q5 Beginning with the second-order differental equation of the deflection curve (the bending moment equation) (5 1) determine the reactions, shear forces, bending moments, slopes, and deflections of the beam construct the shear-force and bending-moment diagrams, labelling all critical ordinates (5 2) Mg Mv Rs L RA Figure Q5 Fixed-end beam

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter10: Statically Indeterminate Beams

Section: Chapter Questions

Problem 10.3.4P: A fixed-end beam AB of a length L supports a uniform load of intensity q (see figure). Beginning...

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A fixed-end beam AB of a length L supports a uniform load of intensity q (see figure). Beginning with the second-order differential equation of the deflection curve (the bending-moment equation), obtain the reactions, shear forces, bending moments, slopes, and deflections of the beam. Construct the shear-force and bending-moment diagrams, Labeling all critical ordinales.
-22 Derive the equations of the deflection curve for a simple beam AB with a distributed load of peak intensity q0acting over the left-hand half of the span (see figure). Also, determine the deflection cat the midpoint of the beam. Use the second-order differential equation of the deflection curve.
A propped cantilever beam of a length L is loaded by a concentrated moment M0at midpoint C Use the second-order differential equation of the deflection curve to solve for reactions at A and B. Draw shear-force and bending-moment diagrams for the entire beam. Also find the equations of the deflection curves for both halves of the beam, and draw the deflection curve for the entire beam.
A fixed-end beam AB of a length L is subjected to a uniform load of intensity q acting over the middle region of the beam (sec figure). Obtain a formula for the fixed-end moments MAand MBin terms of the load q, the length L, and the length h of the loaded part of the beam. Plot a graph of the fixed-end moment MAversus the length b of the loaded part of the beam. For convenience, plot the graph in the following nondimensional form: MAqL2/l2versusbL with the ratio b/L varying between its extreme values of 0 and 1. (c) For the special case in which ù = h = L/3, draw the shear-force and bending-moment diagrams for the beam, labeling all critical ordinates.
-6 Calculate the maximum deflection of a uniformly loaded simple beam if the span length L = 2.0 m, the intensity of the uniform load q = 2.0 kN/m, and the maximum bending stress = 60 MPa, The cross section of the beam is square, and the material is aluminum having modulus of elasticity E = 70 GPa. (Use the formulas of Example 9-1.)
-17 A cantilever beam AB is acted upon by a uniformly distributed moment (bending moment, not torque) of intensity m per unit distance along the axis of the beam (see figure). Derive the equation of the deflection curve and then obtain formulas for the deflection Band angle of rotation Bat the free end. Use the second-order differential equation of the deflection curve.
-4-13 A propped cantilever beam of a length 2L is loaded by a uniformly distributed load with intensity q. The beam is supported at B by a linearly elastic spring with stiffness k. Use the method of superposition to solve for all reactions. Also draw shear-force and bending-moment diagrams, labeling all critical ordinates. Let k = 6EI/L3.
A cantilever beam model is often used to represent micro-clectrical-mechanical systems (MEMS) (sec figure}. The cantilever beam is made of polysilicon (E = 150 GPa) and is subjected to an electrostatic moment M applied at the end of the cantilever beam. 1 f dimensions arc h — 2 [im, h — 4 ^m, and L = 520 ^mt find expressions for the tip deflection and rotation of the cantilever beam in terms of moment M.
A two-axle carriage that is part of an over head traveling crane in a testing laboratory moves slowly across a simple beam AB (sec figure). The load transmitted to the beam from the front axle is 2200 lb and from the rear axle is 3800 lb. The weight of the beam itself may be disregarded. Determine the minimum required section modulus S for the beam if the allowable bending stress is 17,0 ksi, the length of the beam is 18 ft, and the wheelbase of the carriage is 5 ft. Select the most economical I-beam (S shape) from Table F-2(a), Appendix F.
-21 Derive the equations of the deflection curve for a cantilever beam AB supporting a distributed load of peak intensity q0acting over one-half of the length (see figure). Also, obtain formulas for the deflections Band cat points B and C, respectively Use the second-order differentia] equation of the deflection curve.
-12 Derive the equation of the deflection curve for a cantilever beam AB supporting a load P at the free end (see figure). Also, determine the deflection Band angle of rotation bat the free end. Use the second-order differential equation of the deflection curve.
A simple beam of length L = 5 m carries a uniform load of intensity q = 5,8 kN/m and a concentrated load 22.5 kN (see figure). (a) Assuming tra]]ow = 110 MPa, calculate the required section modulus S. Then select the most economical wide-flange beam (W shape) from Table F-l(b) in Appendix F, and recalculate S, taking into account the weight of the beam. Select a new beam if necessary. (b) Repeat part (a), but now assume that the design requires that the W shape must be used in weak axis bending (i.e., it must bend about the 2-2 (or y) axis of the cross section).