A beam ABC, having flexural rigidity El = 75 kN.m², is loaded by a force P = 1.2 kN at end C and tieddown at end A by a wire having axial rigidity EA= 900 kN, as shown in figure below. Using thesuperposition method, calculate the deflection and slope at point C.AB0.5 m0.5 m0.75 mDAnswer:5(mm)=5.244e (rad)= 0.00279950X

Step 1: Solve reactive forces Step 2: Compute deflection using integration method Step 3: boundary…

Answered: A beam ABC, having flexural rigidity El…

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 9.6.10P: -10 The simple beam AB shown in the figure supports two equal concentrated loads P: one acting...

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The cantilever beam ACE shown in the figure has FlexuraI rigidity EI = 2,1 x 106kip-in". Calculate the downward deflections Scand 8Sat points C and B, respectively, due to the simultaneous action of the moment of 35 kip-in. applied at point C and the concentrated load of 2,5 kips applied at the free end B.
Beam ACE hangs from two springs, as shown in the figure. The springs have stiffnesses kxand k2and the beam has flex lira I rigidity EL (a) What is the downward displacement of point C, which is at the midpoint of the beam, when the moment M0 is applied? Data for the structure are as follows: M0= 10,0 kN m, L = 1.8 m, EI = 216 kN m2, Jt, = 250 kN/m, and k2= 160 kN/m, (b) Repeat part (a), but remove A/() and apply a uniform load q — 3.5 kN/m to the entire beam.
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Beam ABC is loaded by a uniform load q and point load P at joint C. Using the method of superposition, calculate the deflection at joint C. Assume that L = 4 m, a =2ra, q = 15 kN/m, P = 7.5 kN, £ = 200 GPa, and / = 70.8 X 106 mm4.
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The simply supported beam carries a uniformly distributed load over parts of its length. Compute (a) the midspan slope and deflection, (b) the slope and deflection at point C. Segment AC’s beam property is worth EI and segment BC’s beam property is worth 2EI. E = 200 GPa, I = 80x106 mm4. Solve problem using the Area Moment Method.
For the beam and loading shown, use the double-integration method to determine (a) the equation of the elastic curve for the beam, (b) the slope at A, (c) the slope at B, and (d) the deflection at midspan. Assume that El is constant for the beam. Let Mo = 50KN-m, L= 4.5 m, E= 180 GPa, and I = 115x 106 mm4. Mo B Answer: (b) 0A = i rad (c) Og = i rad (d) vmid = i mm
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Question 2 A beam ABC of length 3m has one support at the left end and the other support at a distance 2m from the left end. The beam carries an uniformly distributed load W=16 kN/m. Given E = 2 x 10$ N/mm? and I = 80 × 106 mm4. a. Find the slopes at the left support A. b. Find the deflection at the right end c. Find the maximum deflection between the supports. W A C 2 m 3 m Figure 2.
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Q 2. Calculate the slope and deflection at the free end of the cantilever beam shown in figure using Method of super position Take. E = 2.05 x 10$ N/mm2 and I = Y x 10% mm“. %3D If the last two digits of student id 2 50, then take Y = last two digits of id /100. If the last two digits of student id < 50, then take Y = last two digits of id /10; If last two digits of id are zeroes, then take Y= 0.75 2 kN 6 kN/m 1.2 kN-m 3 m 2.2 EI
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

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