For the beam and loading shown, use discontinuity functions to compute: (a) the slope B of the beam at B, and (b) the deflection VA of the beam at A. Assume a constant value of EI = 54000 kN-m² for the beam; WA = 15 kN/m, WB = 50 kN/m, LAB = 3.3 m, LBc = 1.9 m. "| WA Answers: (a) OB (b) VA = = LAB *1 1*2 rad. mm. WB B LBC с X

For the beam and loading shown, use discontinuity functions to compute: (a) the slope B of the beam at B, and (b) the deflection VA of the beam at A. Assume a constant value of EI = 54000 kN-m² for the beam; WA = 15 kN/m, WB = 50 kN/m, LAB = 3.3 m, LBc = 1.9 m. "| WA Answers: (a) OB (b) VA = = LAB 1 12 rad. mm. WB B LBC с X

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter9: Deflections Of Beams

Section: Chapter Questions

Problem 9.7.3P: Beam ACB hangs from two springs, as shown in the figure. The springs have stiffnesses Jt(and k2^ and...

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Beam ACB hangs from two springs, as shown in the figure. The springs have stiffnesses Jt(and k2^ and the beam has flexural rigidity EI. What is the downward displacement of point C, which is at the midpoint of the beam, when the moment MQis applied? Data for the structure are M0 = 7.5 kip-ft, L = 6 ft, EI = 520 kip-ft2, kx= 17 kip/ft, and As = 11 kip/ft. Repeat part (a), but remove Af0 and instead apply uniform load q over the entire beam.
A simple beam ACE is constructed with square cross sections and a double taper (see figure). The depth of the beam at the supports is dAand at the midpoint is dc= 2d 4. Each half of the beam has length L. Thus, the depth and moment of inertia / at distance x from the left-hand end are, respectively, in which IAis the moment of inertia at end A of the beam. (These equations are valid for .x between 0 and L, that is, for the left-hand half of the beam.) Obtain equations for the slope and deflection of the left-hand half of the beam due to the uniform load. From the equations in part (a), obtain formulas for the angle of rotation 94at support A and the deflection Scat the midpoint.
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.
For the beam and loading shown, use discontinuity functions to compute(a) the slope of the beam at C (positive if counterclockwise and negative if clockwise).(b) the deflection of the beam at C.Assume LAB = 210 mm, LBC = 140 mm, LCD = 120 mm, LDE = 260 mm, MB = 200 N-m, P = 1080 N and a constant value of EI = 590 × 106 N-mm2 for the beam.
For the beam and loading shown, use discontinuity functions to compute: (a) the deflection VA of the beam at A, and (b) the deflection Vmidspan of the beam at midspan (i.e., x = 2.45 m). Assume a constant value of El = 1270 kN-m² for the beam; M₁ = 9 kN-m, wo = 19.8 kN/m, LAB = 1.1 m, LBc = 2.7 m. MA A Answer: (a) VA = (b) Vmid i LAB i Wo B LBC mm. mm.
For a beam subjected to the load F at the center of the span as shown below, please 1. Find the maximum allowed load F, given a. Modulus of Rupture (MOR) of the material for the beam = 130 GPa b. Beam width b = 0.02m and depth d = 0.05m c. Span length L = 10m 2. If the maximum allowed load F is designed to be 40,000N, given all other conditions the same, what is the minimum MOR required for the material to make the beam? 3. If the maximum allowed load F is designed to be 50,000N, given all other conditions (MOR = 130 GPa) the same, what is the minimum depth d required? F b ✰ d ↓ D L
200 kN/m 140 kN I (m) 5 10 7.5 Figure.2: Encastré beam under variety of loads Your tasks are as follows: 1- Construct free-body diagram (FBD) to show the reaction forces and moments, and the equivalent force of the distributed load, knowing that the upward reaction force on left side is 200 kN and the reaction moment is clockwise with a value of 1300 kN.m. 2- Show FBD for each required section/cut and include the internal forces and moments. 3- Write the distribution functions of the shear force and bending moment for each cut in the heam. 4- By hand construct diagrams for the shear force and bending moment distributions. 5- Determine the magnitudces and positions of maximum shcar force and bending momcnt.
For the simply supported beam subjected to the loading shown, derive equations for the shear force V and the bending moment M for any location in the beam. (Place the origin at point A.) Let a-3.25 m, b=4.75 m, Pg - 35kN, and Pc = 80kN. Construct the shear- force and bending-moment diagrams on paper and use the results to answer the questions in the subsequent parts of this GO exercise. A Ay- 58.66 - Dy- Calculate the reaction forces A, and Dy acting on the beam. Positive values for the reactions are indicated by the directions of the red arrows shown on the free-body diagram below. (Note: Since Ax = 0, it has been omitted from the free-body diagram.) Answers: a 56.33 (a) V= (b) V- (c) V- B i i PB B kN с kN C Determine the shear force acting at each of the following locations: (a) x-2m (b)x - 4 m (c) x-8 m Note that x = 0 at support A. When entering your answers, use the shear-force sign convention detailed in Section 7.2. 3 3 3 KN D b kN D ·x Dy
Problem #5: For the 2D beam below, with F 15 kips, M, = 7 kip-ft, and shear and bending moment diagrams. Report your answer in kip and kip-ft to one decimal place. w,= 2.5 kip/ft draw the Wo F, Fo Mo Mo 2.0 ft 1.0 ft 5.0 ft 2.0 ft By uploading this work, I attest that the work contained herein is solely my own, that I only used the given equation sheet as a reference, and that I have not received any information from anyone else or source regarding this exam at any time.
1. Draw shear and moment bending diagrams for the beam below: the stress caused by an internal moment in a cantilever beam. Lab #4-BENDING STRESS 1.0 INTRODUCTION a 2.0 PROCEDURE O.47 0.52 m J MY 2, Find the moment 0.05 m from the left. 3. Calculate the moment of inertia of the beam. 0.025 m bh bh %3D 12 12 0.021 m 0.025 m
Situation 2 | Beam ABCDEFG below is subjected to multiple loads as show. The total length of the beam is 10m. Analyze the beam completely. 6 kN 10 kN 3 kN/m 2 kN 5 kN-m G 3000mm. 1000mm 1000mm. 2000mm. 1000mm 2000mm.
The simply supported beam consists of a W14 x 34 structural steel wide-flange shape [E = 29,000 ksi; / = 340 in.4]. For the loading shown, use discontinuity functions to compute (a) the slope of the bearn at E and (b) the deflection of the beam at C. Assume wo = 12 kips/ft, wcD = 4.0 kips/ft, LAB= 8.0 ft. LBc= 8.0 ft. Lco - 11.0 ft. LDE = 4 ft. Answer: (a) 8E= (b) vc= B LAB Wo LBC C rad in. WCD LCD D LDE E X