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-23 The beam shown in the figure has a sliding support at A and a roller support at B. The sliding support permits vertical movement but no rotation. Derive the equation of the deflection curve and determine the deflection
Derive the equations of the deflection curve and determine the deflection
Answer to Problem 9.3.23P
Equations of deflection curve:
For
For
For
Deflection at end A,
Deflection at point C,
Explanation of Solution
Given:
For
B.C 1:
Therefore,
For
For
B.C 2:
Therefore,
B.C 3:
Therefore,
B.C 4:
Therefore,
B.C 5:
Therefore,
B.C 6:
From (1) − (5):
For
For
For
So,
And
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Chapter 9 Solutions
Mechanics of Materials (MindTap Course List)
- -18 The beam shown in the figure has a sliding support at A and a spring support at B, The sliding support permits vertical movement but no rotation. Derive the equation of the deflection curve and determine the deflection Bat end B due to the uniform load of intensity q. Use the second-order differential equation of the deflection curve.arrow_forwardThe cantilever beam ACB shown in the figure supports a uniform load of intensity q throughout its length. The beam has moments of inertia I2and IYin parts AC and CB, respectively. Using the method of superposition, determine the deflection SBat the free end due to the uniform load. Determine the ratio r of the deflection 6Bto the deflection 3Xat the free end of a prismatic cantilever with moment of inertia /] carrying the same load. Plot a graph of the deflection ratio r versus the ratio 12 //t of the moments of inertia. (Let 7, tlxvary from I to 5.)arrow_forward-10 Derive the equations of the deflection curve for beam AB with sliding support at A and roller support at B, supporting a distributed load of maximum intensity q0acting on the right-hand half of the beam (see figure). Also, determine deflection A, angle of rotation B , and deflection cat the midpoint. Use the fourth-order differential equation of the deflection curve (the load equation).arrow_forward
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- -2 A simple beam AB is subjected to a distributed load of intensity q(x) = q0sin x/L, where q0is the maximum intensity of the load (see figure). Derive the equation of the deflection curve, and then determine the deflection max at the midpoint of the beam. Use the fourth-order differential equation of the deflection curve (the load equation).arrow_forward-33 Find the horizontal deflection hand vertical deflection vat the free end C of the frame ABC shown in the figure. (The flexural rigidity EI is constant throughout the frame.) Note: Disregard the effects of axial deformations and consider only the effects of bending due to the load P.arrow_forward-6 A cantilever beam .4B is subjected to a parabolically valying load of intensity q(x)=q0(L2x2)/L2 where q0is the maximum intensity of the load (see figure). Derive the equation of the deflection curve, and then determine the deflection Band angle of rotation Bat the free end. Use the fourth-order differential equation of the deflection curve (the load equation).arrow_forward
- Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning