A composite beam is made of two brass [E = 98 GPa] plates bonded to an aluminum [E = 60 GPa] bar, as shown. The beam is subjected to a bending moment of 2270 N-m acting about the z axis. Assume b=44 mm, d₁=25 mm, d₂-8 mm. Determine: (a) the maximum bending stresses Obr, Gal in the brass plates and the aluminum bar. (b) the stress in the brass brj at the joints where the two materials are bonded together. Z Brass (2) Aluminum (1) Brass (2) Answers: (a) Obr (b) 6 brj = i i b d₂ d₁ d₂ MPa, Gal = i MPa. MPa.
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- 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 plastic-lined steel pipe has the cross-sectional shape shown in the figure. The steel pipe has an outer diameter d1= 100 mm and an inner diameter d2= 94 mm. The plastic liner has an inner diameter d1= 82 mm. The modulus of elasticity of the steel is 75 times the modulus of the plastic. Determine the allowable bending moment Mallowif the allowable stress in the steel is 35 M Pa and in the plastic is 600 kPa. If pipe and liner diameters remain unchanged, what new value of allowable stress for the steel pipe will result in the steel pipe and plastic liner reaching their allowable stress values under the same maximum moment (i.e., a balanced design)? What is the new maximum moment?The cross section of a sand wie h beam consisting of aluminum alloy faces and a foam core is shown in the figure. The width b of the beam is 8.0 in, the thickness I of the faces is 0.25 in., and the height hcof the core is 5.5 in. (total height h = 6.0 in). The moduli of elasticity are 10.5 × 106 psi for the aluminum faces and 12.000 psi for the foam core. A bending moment M = 40 kip-in. acts about the z axis. Determine the maximum stresses in the faces and the core using (a) the general theory for composite beams and (b) the approximate theory for sandwich beams.
- A composite beam is made of two brass [E = 97 GPa] plates bonded to an aluminum [E = 62 GPa] bar, as shown. The beam is subjected to a bending moment of 1690 N-m acting about the z axis. Assume b=61 mm, d,=47 mm, d2=10 mm. Determine: (a) the maximum bending stresses opr, oat in the brass plates and the aluminum bar. (b) the stress in the brass oprj at the joints where the two materials are bonded together. Brass (2) Aluminum (1) Brass (2) d2 b Answers: (a) Obr MPa, oal = i MPa. %3D (b) Obrj = MPa.A composite beam is made of two brass [E = 112 GPa] plates bonded to an aluminum [E = 64 GPa] bar, as shown. The beam is subjected to a bending moment of 2230 N-m acting about the z axis. Assume b=48 mm, dz=31 mm, d2=8 mm. Determine: (a) the maximum bending stresses opy,Ja! in the brass plates and the aluminum bar. (b) the stress in the brass obrj at the joints where the two materials are bonded together. Brass (2) dz Aluminum (1) Brass (2) dz b Answers: (a) Obr i MPa, oal = i MPa. (b) Obrj = MPa.A composite beam is made of two brass [E = 97 GPa] plates bonded to an aluminum [E = 70 GPa] bar, as shown. The beam is subjectedto a bending moment of 2140 N-m acting about the z axis. Assume b=44 mm, d =50 mm, d =10 mm. Determine:(a) the maximum bending stresses , in the brass plates and the aluminum bar.(b) the stress in the brass at the joints where the two materials are bonded together.
- A composite beam is made of two brass [E = 107 GPa] plates bonded to an aluminum [E = 65 GPa] bar, as shown. The beam is subjected %3! to a bending moment of 1890 N-m acting about the z axis. Assume b=59 mm, d,=49 mm, d2=10 mm. Determine: (a) the maximum bending stresses opr, oal in the brass plates and the aluminum bar. (b) the stress in the brass obrj at the joints where the two materials are bonded together. Brass (2) dz Aluminum (1) Brass (2) dz b Answers: (a) Obr = i MPa, oal = i MPa. (b) Obri i MPа.A composite beam is made of two brass [E = 98 GPa] plates bonded to an aluminum [E = 64 GPa] bar, as shown. The beam is subjected to a bending moment of 1560 N-m acting about the z axis. If the moment of inertia about the z axis of the equivalent all-aluminum beam is 737760 mm 4, find the maximum bending stress in the aluminum plate. Brass Aluminum Brass O 43.0 MPa O 37.6 MPa O 23.5 MPa O 31.7 MPa O 34.3 MPa 50 mm 10 mm 30 mm 10 mmA composite beam is made of two brass [E = 95 GPa] plates bonded to an aluminum [E = 75 GPa] bar, as shown. The beam is subjected to a bending moment of 1480 N-m acting about the z axis. If the moment of inertia about the z axis of the equivalent all-aluminum beam is 629722 mm4, find the maximum bending stress in the aluminum plate.
- The cross-sectional dimensions of a beam are shown. Assume b-2.125 in., tt-0.3125 in. and d=2.125 in. (a) If the bending stress at point K is 3360 psi (T), determine the internal bending moment M₂ acting about the z centroidal axis of the beam. (b) Determine the bending stress o, at point H (positive if tension, negative if compression). H N K Answers: bf (a) M₂ = i (b) σH = i d lb-ft. psi.An extruded polymer beam is subjected to a bending moment M. The length of the beam is L = 620 mm. The cross-sectional dimensions of the beam are b1 = 39 mm, d1 = 82 mm, b2 = 23 mm, d2 = 23 mm, and a = 8 mm. For this material, the allowable tensile bending stress is 20 MPa, and the allowable compressive bending stress is 12 MPa. Determine the largest moment M that can be applied as shown to the beam.A composite beam is made of two brass [E =101 GPa] plates bonded to an aluminum [E =64 GPa] bar, as shown in Figure below. The beam is subjected to a bending moment of 2030 N-m acting about the z axis. Assume b=53 mm, d1=52 mm, d2 =11 mm, Determine: (a)the maximum bending stresses in the brass plates and the aluminum bar. (b) the stress in the brass at the joints where the two materials are bonded together.