Tut 1 - Stress & Strain

Tut 1 - Stress & Strain - Tutorial 1 STRESS AND...

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Tutorial 1: STRESS AND STRAIN 1. The steel tie bar shown is to be designed to carry a tension force of magnitude 120 kN when bolted between double brackets at A and B. The bar will be fabricated from 20 mm thick plate stock. The maximum allowable stresses for the bolt material are: τ = 100 MPa and σ = 350 MPa. Calculate (i) the smallest allowable diameter d of the bolt; (ii) the corresponding bearing stress between the 20 mm thick plate and the bolt. Ans: 27.6 mm; 217 MPa. 2. A strain gauge located at C on the surface of bone AB indicates that the average normal stress in the bone is 3.80 MPa when the bone is subjected to two 1200 N forces as shown. Assuming the cross section of the bone at C to be annular and knowing that its outer diameter is 25 mm, determine the inner diameter of the bone’s cross section at C. Ans: 14.9 mm. 3. Two steel plates are to be held together by means of 7 mm diameter high strength steel bolts fitting snugly inside cylindrical brass spacers. Knowing that the average normal stress must not exceed 210 MPa in the bolts and 120 MPa in the spacers, determine the outer diameter of the spacers that yields the most economical and safe design. Ans: 11.6 mm. 4. Two solid cylindrical rods AB and BC are welded together at B and loaded as shown. Knowing that d 1 = 30 mm and d 2 = 50 mm, find the average normal stress in the midsection of (a) rod AB, (b) rod BC. Ans: 84.9 MPa; 96.8 MPa. 5. Determine the diameter of the largest circular hole that can be punched into a sheet of polystyrene 6 mm thick, knowing that the force exerted by the punch is 45 kN and that a 55 MPa average shearing stress is required to cause the material to fail. Answer: 43.4 mm 6. A hydraulic press, which is able to generate a total force of 5 MN, is supported by two similar steel rods. Calculate the diameter of each rod and find the extension of each rod in a length of 1.5 m. The safe stress is 0.85 GPa and E is 207 GPa. Answer: 61.1 mm, 6.16 mm 7. A prismatic bar with rectangular cross section (25 mm x 50 mm) and length L = 3.5 m is subjected to an axial tensile force of 90 kN. The bar is observed to elongate by 1 mm. Calculate the tensile stress and strain in the b a r . Answer: 72. N/mm 2 ; = 0.000286 1200 N 1200 N 60 kN 125 kN 125 kN
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8. A long wire hangs vertically under its own weight. What is the greatest length it can have without breaking if it is made of: (a) steel having an ultimate stress of 2 kN/mm 2 and (b) aluminium having an ultimate stress of 350 N/mm 2 ? (Note: The unit weight of steel is 77 kN/m 3 and of aluminium is 27 kN/m
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This note was uploaded on 05/10/2009 for the course MXXM 2XX9 taught by Professor Gxxy during the Spring '09 term at City University of Hong Kong.

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Tut 1 - Stress & Strain - Tutorial 1 STRESS AND...

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