10.4-29 A propped cantilever beam is loaded by a triangular distributed load from A to C (see figure). The load has a peak intensity qo = 145 N/m. The length of the beam is 3.6 m. Find support reactions at A and B. C В |A 2
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- A beam A BCD rests on simple supports at B and C (see figure). The beam has a slight initial curvature so that end A is 18 mm above the elevation of the supports and end D is 12 mm above. What moments Mtand M^, acting at points A and Dtrespectively, will move points A and D downward to the level of the supports? (The flexural rigidity EI of the beam is 2.5 X 106 N m2 and L = 2.5m).Two flat beams AB and CD, lying in horizontal planes, cross at right angles and jointly support a vertical load P at their midpoints (see figure). Before the load P is applied, the beams just touch each other. Both beams are made of the same material and have the same widths. Also, the ends of both beams are simply supported. The lengths of beams AB and CD are LABand LCD, respectively. What should be the ratio tABltCDof the thicknesses of the beams if all four reactions arc to be the same?Beam ABC is fixed at support A and rests (at point B) upon the midpoint of beam DE (see part a of the figure). Thus, beam, ABC may be represented as a propped cantilever beam with an overhang BC and a linearly elastic support of stiffness k at point B (see part b of the figure). The distance from A to B is L = 10 ft, the distance from B to C is L/2 = 5 ft, and the length of beam DE is L = 10 ft. Both beams have the same flexural rigidity EI. A concentrated load P = 1700 lb acts at t lie free end of beam ABC. Determine the reactions RA, RB+ and MAfor beam ABC. Also, draw the shear-force and bending-moment diagrams for beam ABC, labeling all critical ordinates.
- A fixed-end beam is loaded by a uniform load q = 15 kN/m and a point load P = 30 kN at mid-span. The beam has a length of 4 m and modulus of elasticity of 205 GPa. Find reactions at A and B. Calculate the height of the beam if the displacement at mid-span is known to be 3 mm. Assume that the beam has rectangular cross section with h/b = 2.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.Obtain formulas for the angle of rotation 0Aat support A and the deflection SajAXat the midpoint for a simple beam AB with a uniform load of intensity q (see figure).
- A singly symmetric beam with a T-section (see figure) has cross-sectional dimensions b = 140 mm, a = 190, 8 mm, b. = 6,99 mm, and fc = 11,2 mm. Calculate the plastic modulus Z and the shape factor.The figure shows a nonprismatic, propped cantilever beam AB with flexural rigidity 2EI from A to C and EI from C to B. Determine all reactions of the beam due to the uniform load of intensity q. Hint: Use the results of Problems 9.7-1 and 9.7-2.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.
- 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.A simple beam AB is loaded as shown in the figure. Calculate the required section modulus S if ^aibw = IS,000 psi, L = 32 ft, P = 2900 lb, and g = 450 lb/ft. Then select a suitable I-beam (S shape) from Table F-2(a), Appendix F, and recalculate 5 taking into account the weight of the beam. Select a new beam size if necessary. What is the maximum load P that can be applied to your final beam selection in part (a)?A beam rests on supports at A and B and is loaded by a distributed load with intensity q as shown. A small gap exists between the unloaded beam and the support at C. Assume that span length L = 40 in. and flexural rigidity of the beam EI = 04 x 109lb-in2. Plot a graph of the bending moment at B as a function of the load intensity q. Hint: See Example 9-9 for guidance on computing the deflection at C.