Example (5.3): Find the maximum tensile and compressive stresses for the beam shown in Figure (5.6). 10 KN 2 kN/m 100 mm 50 mm S.E.D (KN) Solution: -10 -14 BM.D(KN.m) -24 Figure (56)
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- A reinforced concrete T-beam (see figure) is acted on by a positive bending moment of M = 175 kip-ft. Steel reinforcement consists of four bars of 1.41-inch diameter. The modulus of elasticity for the concrete is Ec= 3000 ksi while that of the steel is £s = 29,000 ksi. Let b = 48 im, rf = 4 in., bw=15 in,, and d = 24 in, Find the maximum stresses in steel and concrete, If allowable stresses for concrete and steel are o"ac = 1400 psi and tr^ =18 ksi, respectively, what is the maximum permissible positive bending moment?A bimetallic beam used in a temperature-control switch consists of strips of aluminum and copper bonded together as shown in the figure, which is a cross-sectional view. The width of the beam is LO in,, and each strip has a thickness of 1/16 in. Under the action of a bending moment M = 12 lb-in, acting about the z axis, what are the maximum stresses aaand ecin the aluminum and copper, respectively? (Assume fA, = 10,5 x l0 psi and ecu= 16,8 × 106 psi,)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 B
- Beam ABC with an overhang BC is subjected to a linearly varying distributed load on span AB with peak: intensity q0= 2500 N/m and a point load P = 1250 N applied at C. The beam has a width ft = 100 mm and depth h = 200 mm. Find the state of plane stress at point D located 150 mm below the top of the beam and 0.2 m to the left of point B. Also find the principal stresses at D>Neglect the weight 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 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 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 wood beam with a rectangular cross section (see figure) is simply supported on a span of length L. The longitudinal axis of the beam is horizontal, and the cross section is tilted at an angle a. The load on the beam is a vertical uniform load of intensity q acting through the centroid C. Determine the orientation of the neutral axis and calculate the maximum tensile stress bmaxif PROBLEMS 6.4-2 and 6.4-3 b = 80 mm, b = 140 mm, L = 1,75 m, a — 22.5°, and q = 7.5 kN/m.Solve 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.
- 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 W 12 x 35 steel beam is fixed at A. The beam has length L = 6 ft and is subjected to a linearly varying distributed load with peak intensity q0=830 lb/ft. Calculate the state of plane stress at point C located 3 in, below the top of the beam at mid-span. Also find the principal normal stresses and the maximum shear stress at C. Include the weight of the beam. Sec Table F-l(a), Appendix F, for beam propertiesA W 200 x 41.7 wide-flange beam (see Table F-l(b), Appendix F) is simply supported with a span length of 2.5 m (see figure). The beam supports a concentrated load of 100 kN at 0.9 m from support B. At a cross section located 0,7 m from the left-hand support, determine the principal stresses tr, and 2and the maximum shear stress rnMJt at each of the following locations: (a) the top of the beam, (b) the top of the web, and (c) the neutral axis,