stress and strain(tut)

# stress and strain(tut) - THE UNIVERSITY OF HONG KONG...

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Unformatted text preview: THE UNIVERSITY OF HONG KONG Faculty of Engineering Foundations of engineering mechanics (ENGGIOIO) Tutorial 3: Introduction to Stress and Strain 1. A wood tension member with a 50 mm x 100 mm rectangular cross section will be fabricated with an inclined glue joint (45“ 5 ¢ 5 90”) at its mid- section, as shown in Figure 1. If the allowable stresses for the glue are 5 MPa in tension and 3 MPa in shear, determine (a) the optimum angle g6 for the joint; and (b) the maximum safe load P for the member. Ans: (a) 59.00, (b) 34.0 kN. Figure 1 2. Rope BD has a strength of 100 kN. The pin at A has a diameter of 10 mm and is made of steel with an ultimate shearing stress of 350 MPa. Determine the safety factor for the loading shown. Note that ABC is not a truss. Ans; rope 3.81,pin3.11. A ” .5bgmm 15kN ‘L 'l—TﬂMImII—I.‘ 701} Illlll —-i Figure 2 3. Three plates are joined with a 12 mm diameter pin, as shown in Figure 3. Determine the maximum load P that can be transmitted by the joint if (a) the maximum axial stress on a cross section at the pin must be limited to 350 MPa; (b) the maximum bearing stress between a plate and the pin must be limited to 650 MPa; m (c) the maximum shearing stress on a cross section PIE of the pin must be limited to 240 MPa; and 25 mm H 10 mm (d) the punching shear resistance of the material in 18 mm the top and bottom plates is 300 MP3. Ans: (a) 113.8 kN, (b) 156 kN, Figure 3 (c) 54.3 kN, (d) 216 kN. 4. The rigid yokes B and C of Figure 4 are securely fastened to the 50 mm square steel (E = 210 GPa) bar AD. Determine (a) the maximum normal stress in the bar; and (b) the change in length of the complete bar. Ans: (a) 148.0 MPa (T), (b) 2.50 mm. 5. Figure 5 depicts an assembly consisting of a steel bolt and an aluminium collar. The pitch of the single l‘__‘5—o—‘_"_‘l threaded bolt is 3 mm and its cross—sectional area is 600 m2. The cross-sectional area of the collar is 900 mmz. The nut is brought to a snug position and then given an additional 1/8 of a turn. Determine the stresses in the aluminium collar and the steel bolt. Given E5 = 200 GPa, EAl = 70 GPa — IH-HIIHHIIIIIJ’. ALUMINIUM COLLAR Figure 5 Ans: 516.4 MPa, -344.3 MPa 6. (a) Show that when a truss (elastic modulus E, cross sectional area A, thermal coefﬁcient of expansion or, length L) is subjected to a tensile force F and temperature change T, its elongation is: o = iL—+ OLLT AE (b) A rigid bar is hanged by three of the trusses described in part (a), as shown in Figure 6. Initially, the bar is horizontal. The truss connected to joint C is then subjected to a temperatlHe rise T , and a downward force P is applied to the rigid bar. Is the problem statically determinate? Determine the tensions in the trusses and also the rotation of the rigid bar. Assume Figure 6 that the rotation is very small. Ans: TA = (7P—20LAET)/12, TB : (P +0LAET)/3, TC = (P—ZorAET)/12 Rotation = a T _ ___P_ in the clockwise direction ZAE 7. Determine the horizontal movement of point A in Figure 7 due to a temperature drop of 450C. Assume that member AE has an insigniﬁcant coefﬁcient of thermal expansion. The coefﬁcients of thermal expansion are 11.9x10'6 / 0C for the steel and 22.5 x 106 / 0C for the aluminum alloy. Ans: 1.27 mm id 300 mm >1 8. A 150 mm diameter by 200 mm long polymer (ED = 2.10 GPa) cylinder is attached to a 45 mm diameter by 400 mm long brass (E, = 100 GPa) rod by using the ﬂange type of connection shown in Figure 8. A 0.15 mm clearance exists between the parts as a result of machining error. If the bolts are inserted and tightened, determine _% |_(_ 0.15 mm (a) the axial stresses produced in each of the members; and (b) the ﬁnal position of the ﬂange—polymer interface after assembly, with respect to the leﬁ support. 400 mm Ans: (a) 1.074 MPa (T), 11.93 MPa (I); (b) 200.1023 mm. Figure 8 ...
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