The extended beam ABC in the figure below is pin-supported at A and roller-supported at B. For the given loading P=2kN A 0.5m 0.5m 0.5m M, 4 kN m
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A: For solution refer below images.
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The beam will fail if the maximum bending moment reaches 900 Nm or the maximum shear force becomes 2500 N. Is the beam safe and why?
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- A cantilever beam(Z, = 6 ft) with a rectangular cross section (/> = 3.5 in., h = 12 in.) supports an upward load P = 35 kips at its free end. (a) Find the state of stress ((7T, o^., and r in ksi) on a plane-stress element at L/2 that is i/ = 8 in. up from the bottom of the beam. Find the principal normal stresses and maximum shear stress. Show these stresses on sketches of properly oriented elements. (b) Repeat part (a) if an axial compressive centroidal load N = 40 kips is added at BSolve the preceding problem for a box beam with dimensions h = 0.5 m, h = 0.18 m, and t = 22 mm. The yield stress of the steel is 210 MPa.Beam AB has an elastic support kR at A, pin support at B, length L, height h (see figure), and is heated in such a manner that the temperature difference T2T1 between the bottom and top of the beam is proportional to the distance from support A. Assume the temperature difference varies linearly along the beam: T2T1=T0x in which T0 is a constant having units of temperature (degrees) per unit distance. Assume the spring at A is unaffected by the temperature change. Determine the maximum deflection max of the beam, Repeat for a quadratic temperature variation along the beam, so T2T1=T0x2 What is max for parts (a) and (b) if kR goes to infinity?
- A simple beam thai is IS ft long supports a uni¬form load of intensity a. The beam is constructed of two angle sections, each L (1 × 4 × 1/2, on either side of a 2 in. x 8 in. (actual dimensions! wood beam (see the cross section shown in the figure part a]. The modulus of elasticity of the s I eel is 10 limes that of the wood, (a) If the allowable stresses in the steel and wood are 12,000 psi and 900 psi. respectively, what is the allow atile load a t. A olc. Disregard the weight of the beam, and see Table F-5(a) of Appendix I ' for I lie dimensions and properties of the angles. (b) Repeal partial if a I in. 10 in. wood Hange tactual dimensions) is added i see figure pallhi b).A simple beam with an overhang is subjected to d point load P = 6kN. If the maximum allowable deflect ion at point C is 0.5 mm, select the lightest W360 section from Table F-l{b) that can be used for the beam. Assume that L = 3 m and ignore the distributed weight of the beam.A propped cantilever beam, fixed at the left-hand end A and simply supported at the right-hand end B, is subjected to a temperature differentia] with temperature T1on its upper surface and T2on its lower surface (see figure).
- A cantilever beam of length L = 2 m supports a load P = 8,0 kN (sec figure). The beam is made of wood with cross-sectional dimensions 120 mm x 200 mm. Calculate the shear stresses due to the load/"at points located 25 mm, 50 mm, 75 mm, and 100 mm from the top surface of the beam. From these results, plot a graph showing the distribution of shear stresses from top to bottom of the beam.A W 12 x 35 steel cantilever beam is subjected to an axial load P = 10 kips and a transverse load V = 15 kips. The beam has length L = 6 ft, (a) Calculate the principal normal stresses and the maximum shear stress for an clement located at C near the fixed support. Neglect the weight of the beam, (b) Repeat Part a for point D which is 4 in. above point C (see figure). See Table F-l(a), Appendix F, for beam properties.A steel bracket of solid circular cross section is subjected to two loads, each of which is P = 4.5 kN at D (see figure). Let the dimension variable be b = 240 mm. Find the minimum permissible diameter dmaxof the bracket if the allowable normal stress is 110 M Pa. Repeat part (a), including the weight of the bracket. The weight density of steel is 77.0 kN/m3.
- A steel plate (called a cover ploie) having cross-sectional dimensions 6,0 in. × 0.5 in. is welded along the full length of the bottom flange of a W 12 × 50 wide-flange beam (sec figure, which shows the beam cross section). What is the percent increase in the smaller section modulus (as compared to the wide-flange beam alone)?Each girder of the lift bridge (sec figure) is 180 ft long and simply supported at the ends. The design load for each girder is a uniform load of intensity 1,6 kips/ft. The girders are fabricated by welding three steel plates to form an I-shaped cross section (see figure) having section modulus S = 3600 in3. What is the maximum bending stress rmaxin a girder due to the uniform load?A square wood platform is 8 ft × 8 ft in area and rests on masonry walls (see figure). The deck of the platform is constructed of 2-in. nominal thickness tongue-and-groove planks (actual thickness 1.5 in.; sec Appendix CL) supported on two S-ft long beams. The beams have 4 in. × (i in. nominal dimensions (actual dimensions 3.5 in. × 5.5 in.). The planks arc designed to support a uniformly distributed load n ( lb/ft" i acting over the entire top surface of the platform. I be allowable bending stress for the planks is 2400 psi and the allowable shear stress is 100 psi. W ben analyzing the planks, disregard their weights and assume that their reactions are uniformly distributed over the top surfaces of the supporting beams. (a) Determine the allowable platform load Mr. (lb/ft2) based upon the bending stress in the planks. (b) Determine the allowable platform load if-. (lb/ft-) based upon the shear stress in the planks. (c) Which of the preceding values becomes the allowable load alolow on the platform? Hints: Use care in constructing the loading diagram for the planks, noting especially that the reactions are distributed loads instead of concentrated loads. Also, note that the maximum shear forces occur at the inside faces of the supporting beams.