A bimetallic beam used in a temperature-control switch consists of strips of aluminum and coppe bonded together as shown in the figure, which is a cross-sectional view. The width of the beam i 1.0 in., and each strip has a thickness of 1/16 in. Under the action of a bending moment M =22.5 Ib-in. acting about the z axis, what are the maximum stresses oą and o, in the aluminum and copper, respectively? (Assume Ea = 10.5 x %3D 106 psi and E. = 16.8x 106 psi .) %3D
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A: For solution refer below images.
M=22.5 ib-in
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- A simple beam of span length 3.2 m carries a uniform load of intensity 48 kN/m, The cross section of the beam is a hollow box with wood flanges and steel side plates, as shown in the figure. The wood flanges are 75 mm x 100 mm in cross section, and the steel plates are 300 mm deep. What is the required thickness t of the steel plates if the allowable stresses are 120 M Pa for the steel and 6,5 M Pa for the wood? (Assume that the moduli of elasticity for the steel and wood are 210 GPa and 10 GPa, respectively, and disregard the weight of the beam.)A wood beam reinforced by an aluminum channel section is shown in the figure. The beam has a cross section of dimensions 150 mm x 250 mm, and the channel has a uniform thickness of 6.5 mm. If the allowable stresses in the wood and aluminum are 8 M Pa and 38 M Pa, respectively, and if their moduli of elasticity are in the ratio 1 to 6, what is the maximum allowable bending moment for the beam?The composite beam shown in the figure is simply supported and carries a total uniform load of 40 kN/m on a span length of 4.0 m. The beam is built of a southern pine wood member having cross-sectional dimensions of 150 mm × 250 mm and two brass plates of cross-sectional dimensions 30 mm × 150 mm. Determine the maximum stresses (7b and ctwin the brass and wood, respectively, if the moduli of elasticity are EB= % GPa and Ew= 14 GPa. (Disregard the weight of the beam.) Find the required thickness of the brass plates so that the plate and wood reach their allowable stress values of Eb= 70 MPa and t Ew= 8.5 MPa simultaneously under the maximum moment. What is the maximum moment?
- A reinforced concrete slab (see figure) is reinforced with 13-mm bars spaced 160 mm apart at d = 105 mm from the top of the slab. The modulus of elasticity for the concrete is Ec= 25 GPa, while that of the steel is £s = 200 G Pa. Assume that allowable stresses for concrete and steel arecrac = 9.2 MPa and us = 135 MPa. l()5 mm Find the maximum permissible positive bending moment for a l-m wide strip of the slab. What is the required area of steel reinforcement, A^ if a balanced condition must be achieved? What is the allowable positive bending moment? (Recall that in a balanced design, both steel and concrete reach allowable stress values simultaneously under the design moment.)A composite beam consisting of fiberglass faces and a core of particle board has the cross section shown in the figure. The width of the beam is 2,0 in., the thickness of the faces is 0,10 in., and the thickness of the core is 0.50 in. The beam is subjected to a bending moment of 250 lb-in, acting about the - axis. Find the maximum bending stresses tr(and ctc in the faces and the core, respectively, if their respective moduli of elasticity are 4 x 106 psi and 1.5 x 106 psi.A simple beam with a rectangular cross section (width, 3,5 inL; height, 12 in,) carries a trapczoi-dally distributed load of 1400 lb/ft at A and 1000 lb/ft at B on a span of 14 ft (sec figure). Find the principal stresses 2 and the maximum shear stress r__ at a cross section 2 ft from the left-hand support at each of the locations: (a) the neutral axis, (b) 2 in. above the neutral axis, and (c) the top of the beam. (Disregard the direct compressive stresses produced by the uniform load bearing against the top of the beam.)
- A steel beam of length L = 16 in. and cross-sectional dimensions h = 0.6 in. and h = 2 in. (see figure) supports a uniform load of intensity if = 240 lb/in., which includes the weight of the beam. Calculate the shear stresses in the beam (at the cross section of maximum shear force) at points located 1/4 in., 1/2 in., 3/4 in., and I in, from the top surface of the beam. From these calculations, plot a graph showing the distribution of shear stresses from top to bottom of the beam.A W 12 x 50 steel wide-flange beam and a segment of a 4-inch thick concrete slab (see figure) jointly resist a positive bending moment of 95 kip-ft. The beam and slab are joined by shear connectors that are welded to the steel beam. (These connectors resist the horizontal shear at the contact surface.) The moduli of elasticity of the steel and the concrete are in the ratio 12 to 1. Determine the maximum stresses r1 and xtin the steel and concrete, respectively. Note: See Table F-l(a) of Appendix F for the dimensions and properties of the steel beam.A r o lukI f/frm f «m t ub e of ou t sid e d ia met er ^ and a copper core of diameter dxare bonded to form a composite beam, as shown in the figure, (a) Derive formulas for the allowable bending moment M that can be carried by the beam based upon an allowable stress <7Ti in the titanium and an allowable stress (u in the copper (Assume that the moduli of elasticity for the titanium and copper are Er- and £Cu, respectively.) (b) If d1= 40 mm, d{= 36 mm, ETl= 120 GPa, ECu= 110 GPa, o-Ti = 840 MPa, and ctqj = 700 MPa, what is the maximum bending moment Ml (c) What new value of copper diameter dtwill result in a balanced design? (i.e., a balanced design is that in which titanium and copper reach allow- able stress values at the same time).
- A simple beam that is 18 ft long supports a uniform load of intensity q. The beam is constructed of two C8 x 11.5 sections (channel sections or C-shapes) on either side of a 4 × 8 (actual dimensions) wood beam (see the cross section shown in the figure part a). The modulus of elasticity of the steel (E; = 30,000 ksi) is 20 times that of the wood (Ew). (a) If the allowable stresses in the steel and wood are 12,000 psi and 900 psi, respectively, what is the allowable load qmax Note: Disregard the weight of the beam, and see Table F-3(a) of Appendix F for the dimensions and properties of the C-shape beam. (b) If the beam is rotated 90° to bend about its v axis (see figure part b) and uniform load q = 250 lb/ft is applied, find the maximum stresses trs and crw in the steel and wood, respectively Include the weight of the beam. (Assume weight densities of 35 lb/ft3 and 490 lb/ft3 for the wood and steel, respectively.)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 BA wood beam AB on simple supports with span length equal to 10 ft is subjected to a uniform load of intensity 125 lb/ft acting along the entire length of the beam, a concentrated load of magnitude 7500 lb acting at a point 3 ft from the right-hand support, and a moment at A of 18,500 ft-lb (sec figure). The allowable stresses in bending and shear, respectively, are 2250 psi and 160 psi. From the table in Appendix G, select the lightest beam that will support the loads (disregard the weight of the beam). Taking into account the weight of the beam (weight density = 35 lb/ft3), verify that the selected beam is satisfactory, or if it is not, select a new beam.