Answered: Brass (2) Aluminum (1) Brass (2) b d₂…

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Brass (2) Aluminum (1) Brass (2) b d₂ d₁ d₂

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter6: Stresses In Beams (advanced Topics)

Section: Chapter Questions

Problem 6.2.10P: The cross section of a sandwich beam consisting of fiberglass faces and a lightweight plastic core...

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Concept explainers

Combined Loading

Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial forces, torsion, and so on, then such body is said to be under combined loading. A very practical example of combined loading is the crankshaft of an internal combustion engine (IC engine). The crankshaft of the IC engine is under high rpm, which is caused due to the torsional forces. Due to the presence of piston, counterbalances, and internal imbalances, the crankshaft experiences lateral forces and due to the rise in temperature, the crankshaft undergoes thermal expansion, which pulls the crankshaft along the axial direction and lateral direction. The presence of unbalanced loads along the periphery of the crankshaft also induces a bending moment.

Question

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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 subjected
to 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.

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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) Obrj = i i b d₂ d₁ d₂ MPa, Gal = MPa. i MPa.
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.
Answer the following:
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 = 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 = 95 GPa] plates bonded to an aluminum [E = 74 GPa] bar, as shown. The beam is subjected to a bending moment of 1715 N-m acting about the z axis. If the moment of inertia about the z axis of the equivalent all-aluminum beam is 636712 mm4, find the maximum bending stress in the aluminum plate. Brass Aluminum Brass O 29.5 MPa O 36.6 MPa O 46.6 MPa O 40.4 MPa O 25.1 MPa 50 mm 10 mm 30 mm 10 mm
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 mm
A 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.
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.
An extruded polymer beam is subjected to a bending moment M. The length of the beam is L = 500 mm. The cross-sectional dimensions of the beam are b1 = 35 mm, d1 = 115 mm, b2 = 21 mm, d2 = 21 mm, and a = 7 mm. For this material, the allowable tensile bending stress is 15 MPa, and the allowable compressive bending stress is 14 MPa. Determine the largest moment M that can be applied as shown to the beam. b2 a M d2 d1 A B L b1 Answer: M = i N-m
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.