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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- The cross section of a sandwich beam consisting of fiberglass faces and a lightweight plastic core is shown in the figure. The width b of the beam is 50 mm, the thickness I of the faces is 4 mm, and the height hcof the core is 92 mm (total height A = 100 mm). The moduli of elasticity are 75 GPa for the fiberglass and 1.2 GPa for the plastic. A bending moment M = 275 N · m 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 =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.A beam has a bending moment of 3.5 kN-m applied to a section with a hollow circular cross-section of external diameter 3 cm and internal diameter 2.3 cm . The modulus of elasticity for the material is 210 x 109 N/m2. Calculate the radius of curvature and maximum bending stress. Also, calculate the stress at the point at 0.6 cm from the neutral axis (i) The moment of inertia in (mm^4)= ii) The radius of curvature in (mm) = (iii) The maximum bending stress in (N/mm^2)= iv) The bending stress at the point 0.6 cm from the neutral axis in (N/mm^2)=
- 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.The structure shown below consists of a brass core inserted into a steel tube of cross section square. If a moment of 8 kN × m is applied at its end, determine the maximum bending stress in the bar. Elaton = 100 GPa, Steel = 200 GPa.1. A thin high-strength steel plate having a thickness of 40 mm has a height of 120 mm and length of 350 mm, is subjected to a moment at both ends = 66 kN.m. E = 28000 MPa Determine the bending stress of the steel plate in MPa a. 1440 b. 1855 c. 1344 d. 2063 e. 2333 Determine its radius of curvature in mm. a. 272 b. 558 c. 154 d. 434 e. 166 2. According the NSCP 2015, the first hoop for beams and girders shall be located not more than 50 mm from the face of the supporting columns. The maximum spacing of hoops shall not exceed... a. 150mm b. d/4 c 6 times bar diameter d. all of the above 3. Based on NSCP 2015 Seismic requirement on concrete girders (beams with special moment frames, which of the following most nearly gives the required width (bw) of beam if its overall height is 600 mm. a. 250mm b. 180mm c. 300mm d. 350mm e. 400mm PLEASE ANSWER ALL
- A steel bar of 0.8 x 2.5-in. rectangular cross section is subjected to two equal and opposite couples acting in the vertical plane of symmetry of the bar (Fig. . Determine the value of the bending moment M that causes the bar to yield. Assume σY= 36 ksiN for Newton, m for meter, mm for millimeter, N/(mm^2) for Stress, mm^2 or m^2 for Area, mm^4 for Moment of inertia and Nm for bending moment. Use brackets if the power is MINUS for Example: 0.00125 N =1.25*10^(-3)N. A beam has a bending moment of 3 kN-m applied to a section with a hollow circular cross-section of external diameter 3.4 cm and internal diameter 2.4 cm . The modulus of elasticity for the material is 210 x 109 N/m2. Calculate the radius of curvature and maximum bending stress. Also, calculate the stress at the point at 0.6 cm from the neutral axis Solution: (i) The moment of inertia = ii) The radius of curvature is (iii) The maximum bending stress is iv) The bending stress at the point 0.6 cm from the neutral axis isA 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.
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