6) For the beam below, use the method of superposition to calculate the deflection at C and the slope at A. P P P B CV D A E aa a -a→
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- The deflection curve for a cantilever beam AB (see figure) is given by v=q0x2360L2EI(45L440L3x+15L2x2x4) Describe the load acting on the beam. Determine the reactions RAand M 4at the support.A simple beam ABC DE supports a uniform load of intensity iy (see figure). The moment of inertia in the central part of the beam (BCD) is twice the moment of inertia in the end parts (AB and DE). Find the deflection Scat the midpoint C of the beam. (Obtain the solution by using the modified form of Castigliano's theorem.)-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.
- -10 The simple beam AB shown in the figure supports two equal concentrated loads P: one acting downward and the other upward. Determine the angle of rotation A at the left-hand end, the deflection 1under the downward load, and the deflection 2 at the midpoint of the beam.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.-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.
- A symmetric beam A BCD with overhangs at both ends supports a uniform load of intensity q (see figure). Determine the deflection SDat the end of the overhang. (Obtain the solution by using the modified form of Castiglianos theorem.)A simple beam ABC has a moment of inertia 1,5 from A to B and A from B to C (see figure). A concentrated load P acts at point B. Obtain the equations of the deflection curves for both parts of the beam. From the equations, determine the angles of rotation 0Aand Bcat the supports and the deflection 6Bat point B.-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).
- A cantilever beam has two triangular loads as shown in the figure. Find an expression for beam deflection Scusing Superposition. Find the required magnitude of load intensity q2in terms of q0so that the deflection at C is zero. Find an expression for the deflection at C if both load intensities, qxand q2, are equal to q0.-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 cantilever beam of a length L = 2.5 ft has a rectangular cross section {b = 4in,, h = Sin,) and modulus E = 10,000 ksi. The beam is subjected to a linearly varying distributed load with a peak intensity qQ= 900 lb/ft. Use the method of superposition and Cases 1 and 9 in Table H-l to calculate the deflection and rotation at B.