Beam A BCD has a sliding support at A, roller supports at C and A and a pin connection at B (see figure). Assume that the beam has a rectangular cross section (b = 4 in., h = 12 in.). Uniform load q acts on ABC and a concentrated moment is applied at D. Let load variable q = 1750 lb/ft, and assume that dimension variable L = 4 ft. First, use statics to confirm the reaction moment at A and the reaction forces at C and A as given in the figure. Then find the ratio of the magnitudes of the principal stresses (crj/os) just left of support Cat a distance d = 8 in. up from the bottom, The pedal and crank are in a horizontal plane and points A and B are located on the top of the crank. The load P = 160 lb acts in the vertical direction and the distances (in the horizontal plane) between the line of action of the load and points A and B are b\ = 5.0 in., h-, = 2.5 in., and/>3 = 1.0 in. Assume that the crank has a solid circular cross section with diameter d = 0.6 in
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Chapter 8 Solutions
Bundle: Mechanics Of Materials, Loose-leaf Version, 9th + Mindtap Engineering, 1 Term (6 Months) Printed Access Card
- Find support reactions at A and D and then calculate the axial force N. shear force 1 and bending moment 11 at mid-span of column BD. Let L = 4 m, q0 = 160N/m, P = 200N, and M0= 380 N .m.arrow_forwardA thin steel beam AB used in conjunction with an electromagnet in a high-energy physics experiment is securely bolted to rigid supports (see figure), A magnetic field produced by coils C results in a force acting on the beam. The force is trapezoidally distributed with maximum intensity q0= 18 kN/m. The length of the beam between supports is L = 200 mm, and the dimension c of the trapezoidal load is 50 mm. The beam has a rectangular cross section with width b = 60 and height h = 20 mm. Determine the maximum bending stress max and the maximum deflection for the beam. (Disregard any effects of axial deformations and consider only the effects of bending. Use E = 200 GPa.)arrow_forwardA 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.arrow_forward
- Beam ABCD represents a reinforced-concrete foundation beam that supports a uniform load of intensity q1= 3500 lb/ft (see figure). Assume that the soil pressure on the underside of the beam is uniformly distributed with intensity q2 Find the shear force VBand bending moment MBat point B. Find the shear force Vmand bending moment M at the midpoint of the beam.arrow_forwardBeam 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.arrow_forwardA 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.arrow_forward
- A foot bridge on a hiking trail is constructed using two timber logs each having a diameter d = 0.5 m (see figure a). The bridge is simply supported and has a length L = 4 m. The top of each log is trimmed to form the walking surface (see Fig, b)LA simplified model of the bridge is shown in Fig. g. Each log must carry its own weight w = 1.2 kN/m and the weight (P = 850 N) of a person at mid-span, (see Fig. b). Determine the maximum tensile and compressive stresses in the beam (Fig, b) due to bending. If load h is unchanged, find the maximum permissible value of load ... if the allowable normal stress in tension and compression is 2.5 M Pa.arrow_forwardBeam ACB hangs from two springs, as shown in the figure. The springs have stiffnesses Jt(and k2^ and the beam has flexural rigidity EI. What is the downward displacement of point C, which is at the midpoint of the beam, when the moment MQis applied? Data for the structure are M0 = 7.5 kip-ft, L = 6 ft, EI = 520 kip-ft2, kx= 17 kip/ft, and As = 11 kip/ft. Repeat part (a), but remove Af0 and instead apply uniform load q over the entire beam.arrow_forwardA cantilever beam of a length L and loaded by a uniform load of intensity q has a fixed support at A and spring support at B with rotational stiffness kR. A rotation B at B results in a reaction moment MB=kRxB. Find rotation B and displacement Bat end B. Use the second-order differential equation of the deflection curve to solve for displacements at end B.arrow_forward
- Solve the preceding problem for a cantilever beam with data as b = 4 in., h = 9 in., L = 10 ft, P = 325 lb, and x = 45°.arrow_forwardA 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.arrow_forwardA compound beam (see figure) has an shear release just to the left of C and a moment release just to the right of C. A plot of the moment diagram is provided below the beam for applied load P at B and triangular distributed loads v(x) on segments Z/C and CD. First, solve for reactions using statics; then plot axial force (A) and shear force (K) diagrams. Confirm that the moment diagram is that shown below. Label all critical N, V, and M values and also the distance to points where N, V, and/or M are zero.arrow_forward
- Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning