The following beam is loaded and has the support conditions as shown in Fig. 1. Consider the value of P is 240 kN and L is 2120 mm. Answer the followings: a. Identify the support types and construct the free-body diagram of ABCD beam. b. Determine the reaction forces at support A, C and D. c. Draw the shear force diagram. d. Draw the bending moment diagram. PL at C PL at B L/2 L/2 L/4 L/4 Fig. 1.
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- -4-4 A cantilever beam is supported at B by cable BC. The beam carries a uniform load q = 200 N/M. If the length of the beam is L = 3 m, find the force in the cable and the reactions at A. Ignore the axial flexibility of the cable.Repeat Problem 11.3-9. Use two C 150 × 12.2 steel shapes and assume that E = 205 GPa and L = 6 m.-15 A composite beam is constructed froma wood beam (3 in. x 6 in.) and a steel plate (3 in, wide). The wood and the steel are securely fastened to act as a single beam. The beam is subjected to a positive bending moment M. = 75 kip-in. Calculate the required thickness of the steel plate based on the following limit states: Allowable compressive stress in the wood = 2 ksi Allowable tensile stress in the wood = 2 ksi Allowable tensile stress in the steel plate = 16 ksi Assume that Ew= 1,500 ksi and es= 30,000 ksi.
- 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 heavy object of weight W is dropped onto the midpoint of a simple beam AB from a height h (see figure). Obtain a formula for the maximum bending stress ^ma* due to tne filing weight in terms of h, st, and 5st, where it is the maximum bending stress and Sstis the deflection at the midpoint when the weight W acts on the beam as a statically applied load. Plot a graph of the ratio o"max/ö"it (that is, the ratio of the dynamic stress to the static stress) versus the ratio iifS^r(Let h/S^ vary from 0 to 10.)Repeat Problem 6.2-1 but now assume that the steel plate is smaller (0.5 in. × 5 in.) and is aligned with the top of the beam as shown in the figure.
- 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)?Beam ABC is loaded by a uniform load q and point load P at joint C. Using the method of superposition, calculate the deflection at joint C. Assume that L = 4 m, a =2ra, q = 15 kN/m, P = 7.5 kN, £ = 200 GPa, and / = 70.8 X 106 mm4.a beam is supported by a pin support at A and a roller support at B. For this question, leave your answer in terms of the variables w and L. (a) Using equilibrium of the full beam, find the support forces at A and B. (b) First section: Make an arbitrary cut between points A and B. Take the distance of the cut to be x along the beam from point A. Draw the free-body diagram for the left section and find functions for the internal shear force, V(x), and bending moment, M(x), in the section of the beam between A and B. (c) Second section: Repeat part (b) for the section of the beam between B and C. Take x to still be the distance from point A. (f) Find the value of x at which V(x) = 0. The internal bending moment reaches a maximum at the same point as V(x) = 0. Find the maximum bending mo- ment. pin Sketch the shear and bending moment diagrams. B L W C roller
- 700N M-150UNm 2m 3m For the above dlagram, given that F, - 450 N. 0-45 degrees and d-5 m calculate the following (neglect the depth of the beam). Note that there is a pin support at A and a roller support at B. The magnitude of the horizontal component of the reaction force at A, Rar. Please provide the answer in Newtons and report to three significant figures. Please Include the unit ("N") within your answer (eg. If the calculated answer was 55.562 Newtons please Input: 55.6 N). Answer: The magnitude of the vertical component of the reaction force at A, Rar. Please provide the answer in Newtons and report to three significant figures. Please include the unit ("N") within your answer (eg. If the calculated answer was 55.562 Newtons please Input: 55.6 N). Answer: The magnitude of the horizontal component of the reaction force at B. Re. Please provide the answer in Newtons and report to three significant figures. Please Include the unit ("N") within your answer (eg. If the calculated…Let a = 4 m, b = 1 m, PB = 30 kN, Pc = 40 kN, and PE = 15 KN. Construct the shear-force and bending-moment diagrams on paper and use the results to answer the questions in the subsequent parts PB B a Pc a PE E Calculate the reaction force Ay acting on the beam. (Note: Since Ax = 0, it has been omitted from the free-body diagram.) Final answer in kN rounded-off to 1 decimal placeThe beam is supported by a pin at point A and a roller at point C. A distributed load is applied to the beam. Neglect the weight and thickness of the beam. Hints: 1. will need to use similar triangles to find the height after sectioning at B. 2. Review direction of normal force, shear force and bending moment and which is positive or negative. W2 W1 A di d2 Values for the figure are given in the following table. Note the figure may not be to scale. Variable Value W1 190 N-m W2 440 N-m di 5 m d2 5 m a. Determine the magnitude of the normal force at point B, NB. . b. Determine the magnitude of the shear force at point B, VB- c. Is the shear force VB a positive or negative shear force? d. Determine the magnitude of the bending moment at point B, MB. e. Is the bending moment MB a positive or negative bending moment? Round your final answers to 3 significant digits/figures.