Calculate the reactions at A and B for the beam subjected to two linearly distributed loads as shown in the figure. 10 kN/m 8 kN/m 4 kN/m 2 kN/m B 4 m 3 m
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Calculate the reactions at A and B for the beam subjected to two linearly distributed loads as shown in the figure.
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- A fixed-end beam AB supports a uniform load of intensity q = 75 lb/ft acting over part of the span. Assume that EI = 300kip-ft2. Calculate the reactions at A and B. Find the maximum displacement and its location. Repeat part (a) if the distributed load is applied from A to B.The cross section of a bimetallic strip is shown in the figure. Assuming that the moduli of elasticity for metals A and B are EA=168 GPa and EB= 90 GPa, respectively, determine the smaller of the two section moduli for the beam. (Recall that section modulus is equal to bending moment divided by maximum bending stress.) In which material does the maximum stress occur?Two identical, simply supported beams AB and CD are placed so that they cross each other at their midpoints (sec figure). Before the uniform load is applied, the beams just touch each other at the crossing point. Determine the maximum bending moments (mab)max* and (MCD)max beams AB and CD, respectively, due to the uniform load if the intensity of the load is q = 6.4 kN/m and the length of each beam is L = 4 m.
- A beam supporting a uniform load of intensity q throughout its length rests on pistons at points A, C and B (sec figure). The cylinders are filled with oil and are connected by a tube so that the oil pressure on each piston is the same. The pistons at A and B have diameter d1and the piston at C has diameter D2. (a) Determine the ratio of d2to d1so that the largest bending moment in the beam is as small as possible. Under these optimum conditions, what is the largest bending moment Mmaxin the beam? What is the difference in elevation between point C and the end supports?A propped cantilever beam is loaded by a triangular distributed load from A to C (sec figure). The load has a peak intensity q0= 10 lb/ft. The length of the beam is 12 ft. Find support reactions at A and B.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.
- The wing of a large commercial jet is represented by a simplified prismatic cantilever beam model with uniform load \v and concentrated loads P at the two engine locations (see figure). Find expressions for the tip deflection and rotation at D in terms of \\\ P, L, and EL.A propped cantilever beam is subjected to two triangularly distributed loads, each with a peak load intensity equal to q0(see figure), lind the expressions for reactions at A and C using superposition. Plot shear and moment diagrams.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.
- Determine the fixed-end moments (MAand MB) and fixed-end forces (R4and Rs) for a beam of length L supporting a triangular load of maximum intensity q0(see figure). Then draw the shear-force and bending-moment diagrams, labeling all critical ordinates.A simple beam AB is subjected to a load in the form of a couple M0 acting at end B (see figure). Determine the angles of rotation A and B at the supports and the deflection at the midpoint.A simple beam AB is subjected to couples M0and 2A0 acting as shown in the figure. Determine the angles of rotation 04and BBat the ends of the beam and the deflection S at point D where the load M0is applied.