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Learning Goal: To apply the flexure formula to beams under load and find unknown stresses, moments, and forces. For straight members having a constant cross-section that is symmetrical with respect to an axis with a moment applied perpendicular to that axis, the maximum normal stress in the cross-section can be calculated using the flexure formula: max = Me where M is the magnitude of the internal moment with respect to the neutral axis, c is the perpendicular distance from the neutral axis to the point farthest from the neutral axis, and I is the moment of inertia of the cross-section about the neutral axis. The maximum normal stress will always occur on the top or bottom surface of the bearn; in fact, one of these surfaces will experience a maximal tensile stress while the other experiences the same magnitude of stress in compression. For points not on a surface of the beam, we can use max/c==0/y to rewrite the flexure formula in the more general form My Figure W σ== W L < 1 of 3 > W Part A - Moment Required to Produce a Given Stress The cross-section of a wooden, built-up beam is shown below. The dimensions are L = 150 mm and w = 15 mm. (Figure 1) Determine the magnitude of the moment M that must be applied to the beam to create a compressive stress of ap=32 MPa at point D. Also calculate the maximum stress developed in the beam. The moment M is applied in the vertical plane about the geometric center of the beam. Express your answers, separated by a comma, to three significant figures. ► View Available Hint(s) M = max = 19.3.38.4 kN-m, MPa Submit Previous Answers Correct Notice how using both forms of the flexure formula simplifies this otherwise-lengthy calculation. ▾ Part B - Minimum Allowable Cross-Section The rod shown in the figure below is supported by smooth journal bearings at A and B that exert only vertical reactions on the shaft. (Figure 2) Determine the smallest allowable diameter of the rod, d, if z = 1.0 m, uy = 11.8 kN/m, and the maximum allowable bending stress is Jallow 150 MPa. Express your answer to three significant figures and include the appropriate units. ▸ View Available Hint(s) Submit μA d = Value • Ć Units ▾ Part C- Absolute Maximum Bending Stress D NOVINY ?
Learning Goal: To apply the flexure formula to beams under load and find unknown stresses, moments, and forces. For straight members having a constant cross-section that is symmetrical with respect to an axis with a moment applied perpendicular to that axis, the maximum normal stress in the cross-section can be calculated using the flexure formula: max = Me ī where M is the magnitude of the internal moment with respect to the neutral axis, c is the perpendicular distance from the neutral axis to the point farthest from the neutral axis, and I is the moment of inertia of the cross-section about the neutral axis. The maximum normal stress will always occur on the top or bottom surface of the beam; in fact, one of these surfaces will experience a maximal tensile stress while the other experiences the same magnitude of stress in compression. For points not on a surface of the beam, we can use max/c=-a/y to rewrite the flexure formula in the more general form σ=- -My Figure Wo 2x BA 2 of 3 > Ød Part B - Minimum Allowable Cross-Section The rod shown in the figure below is supported by smooth journal bearings at A and B that exert only vertical reactions on the shaft. (Figure 2) Determine the smallest allowable diameter of the rod, d, if x = 1.0 m, wo = 11.8 kN/m, and the maximum allowable bending stress is allow = 150 MPa. Express your answer to three significant figures and include the appropriate units. ▸ View Avaliable Hint(s) Submit d= Value 24 Tmax= μA Submit A Part C - Absolute Maximum Bending Stress Provide Feedback C Units Find the absolute maximum bending stress in the beam shown in the figure below. (Eigure 3) The beam has a square cross-section of 7.0 in. on each side, is 16 ft. long, and the initial value of the distributed load is un = 450 lb/ft. Express your answer to three significant figures. ► View Available Hint(s) Avec ? Thonon ? psi Next >
Learning Goal: To apply the flexure formula to beams under load and find unknown stresses, moments, and forces. For straight members having a constant cross-section that is symmetrical with respect to an axis with a moment applied perpendicular to that axis, the maximum normal stress in the cross-section can be calculated using the flexure formula: max = Me ī where M is the magnitude of the internal moment with respect to the neutral axis, c is the perpendicular distance from the neutral axis to the point farthest from the neutral axis, and I is the moment of inertia of the cross-section about the neutral axis. The maximum normal stress will always occur on the top or bottom surface of the beam; in fact, one of these surfaces will experience a maximal tensile stress while the other experiences the same magnitude of stress in compression. For points not on a surface of the beam, we can use max/c=-a/y to rewrite the flexure formula in the more general form σ=- -My Figure Wo <3 of 3 (> Part B - Minimum Allowable Cross-Section The rod shown in the figure below is supported by smooth journal bearings at A and B that exert only vertical reactions on the shaft. (Figure 2) Determine the smallest allowable diameter of the rod, d, if x = 1.0 m, wo = 11.8 kN/m, and the maximum allowable bending stress is allow = 150 MPa. Express your answer to three significant figures and include the appropriate units. ▸ View Avaliable Hint(s) Submit d= Value 24 Tmax= μA Submit A Part C - Absolute Maximum Bending Stress Provide Feedback C Units Find the absolute maximum bending stress in the beam shown in the figure below. (Eigure 3) The beam has a square cross-section of 7.0 in. on each side, is 16 ft. long, and the initial value of the distributed load is un = 450 lb/ft. Express your answer to three significant figures. ► View Available Hint(s) Avec ? Thonon ? psi Next >