Tutorial08 - C(b By superposing the deflection of a simply...

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MEC2025F Mechanics of Solids Tutorial 8: Bending Deflection 20 April 2016 See the recommended reading list in course outline for the sources of the problems. 1 Bending Deflection 1. A simply supported 10 m beam has the loading and dimensions shown. Determine the position and magnitude of the maximum deflection. 2. Determine the midspan deflection of beam AC in terms of the flexural rigidity EI, P and L. 3. A cantilever beam has a second moment of area of 2I in the interval AB and I in the interval BC. Determine the deflection at C. 4. a) Determine expressions for the slope dv dx and the deflection v(x) in the segment AB; and (b) determine the maximum upward deflection of the beam. 5. An aluminium-alloy beam has a second moment of area I = 50 × 10 6 mm 4 and is supported by a pin at A and a 3 m long aluminium rod that is at- tached to the beam at C. The cross-sectional area of the rod CD is 200 mm 2 . Let E a = 70 GPa. (a) Determine the displacement of the beam at
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Unformatted text preview: C. (b) By superposing the deflection of a simply supported flexible beam and the deflection that a rigid beam would experience due to the stretching of rod CD, determine the total deflection at the load point, B. 6. A structural steel shaft of specific weight γ , di-ameter d, and elastic modulus E, is supported by roller bearings at its ends A and B. Determine the maximum permissible length L for this shaft.The deflection of the shaft due to its own weight per unit length w at the midspan is limited to v max . Assumption: Bearings act as simple supports. Given: v max = 5 mm, d = 75 mm, g = 9.81 m.s-2 , γ = 7860 kg.m-3 E = 200 GPa. 7. and 8. A cantilever beam supports a partial uni-form load of intensity w as shown in the next two questions. Determine using moment-area method: (a) The angle of rotation at free end B. (b) The deflection at the free end B. 1...
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