Question 4 Derive the equations of the deflection curve for a simple beam AB loaded by a couple (4 1) Mo acting at distance a from the left-hand support as shown in Figure Q4 Determine the deflection , at the point where the load is applied Use the second- (4 2) order differental equation of the deflection curve Mo A Figure Q4 Simply supported beam with a couple applied at its mid-span

Question 4 Derive the equations of the deflection curve for a simple beam AB loaded by a couple (4 1) Mo acting at distance a from the left-hand support as shown in Figure Q4 Determine the deflection , at the point where the load is applied Use the second- (4 2) order differental equation of the deflection curve Mo A Figure Q4 Simply supported beam with a couple applied at its mid-span

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 9.3.19P: -19 Derive the equations of the deflect ion curve for a simple beam AB loaded by a couple M0acting...

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-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.
-13 Derive the equation of the deflection curve for a simple beam AB loaded by a couple M0at the left-hand support (see figure). Also, determine the maximum deflection max Use the second-order differential equation of the deflection curve.
Derive the equation of the deflection curve for beam AB with sliding support at A and roller at B* carrying a triangularly distributed load of maximum intensity q0(see figure). Also, determine the maximum deflection ôniill of the beam. Lsc the fourth-order differential equation of the deflection curve (the load equation).
-20 Derive the equations of the deflection curve for a cantilever beam AB carrying a uniform load of intensity q over part of the span (see figure). Also, determine the deflection Bat the end of the beam. Use the second-order differential equation of the deflection curve.
A temporary wood flume serving as a channel for irrigation water is shown in the figure. The vertical boards forming the sides of the flume are sunk in the ground, which provides a fixed support. The top of the flume is held by tic rods that are tightened so that there is no deflection of the boards at that point. Thus, the vertical boards may be modeled as a beam AB, supported and loaded as shown in the last part of the figure. Assuming that the thickness t of the boards is 1,5 in., the depth d of the water is 40 in., and the height h to the tie rods is 50 in., what is the maximum bending stress in the boards? Hint: The numerically largest bending moment occurs at the fixed support.
-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).
Use the method of superposition to find the angles of rotation 9Aand SBat the supports, and the maximum deflection for a simply supported beam subjected to symmetric loads P at distance a from each support. Assume that EI is constant, total beam length is L and a = U3. Hint: Use the formulas of Example 9-3.
-14 A cantilever beam AB supporting a triangularly distributed load of maximum intensity q0is shown in the 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.
-9 Derive the equations of the deflection curve for beam ABC with sliding support at A and roller support at B, supporting a uniform load of intensity q acting on the overhang portion of the beam (see figure). Also, determine deflection cand angle of rotation c. Use the fourth-order differential equation of the deflection curve (the load equation).
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.
A counterclockwise moment M0acts at the midpoint of a fixed-end beam ACB of length L (see figure). Beginning with the second-order differential equation of the deflection curve (the bendingmoment equation), determine all reactions of the beam and obtain the equation of the deflection curve for the left-hand half of the beam. Then construct the shear-force and bending-moment diagrams for the entire beam, labeling all critical ordinales. Also, draw the deflection curve for the entire beam.
The equation of the deflection curve for a simply supported beam is v(x)=q024EI(2Lx3x4L3x) Derive the slope equation of the beam. Derive the bending-moment equation of the beam. Derive the shear-force equation of the beam. Describe the loading acting on the beam.