Hw1_Sec(01) - a = 70 GPa α a = 23.6 x 10-6/°C fully...

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2010 - 2011 SPRING SEMESTER AEE 264 Mechanics of Materials Sec(01) HOMEWORK #1 Given: 3 March 2011 Due: 10 March 2011 until 14:40 1. Knowing that the central portion of the link BD has a uniform cross- sectional area of 800 mm 2 , determine the magnitude of the load P for which the normal stress in that portion of BD is 50 MPa. 2. Members AB and BC of the truss shown are made of the same alloy. It is known that a 20-mm-square bar of the same alloy was tested to failure and that an ultimate load of 120 kN was recorded. If a factor of safety of 3.2 is to be achieved for both bars, determine the required cross-sectional area of (a) bar AB , ( b ) bar AC. 3. Each of the links AB and CD is made of aluminum (E = 75GPa) and has a cross-sectional area of 125 mm 2 . Knowing that they support the rigid member BC, determine the deflection of
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Unformatted text preview: a = 70 GPa, α a = 23.6 x 10-6 /°C) fully bonded to a steel core (E s = 200 GPa, α s =11.7 x 10-6 /°C) and is unstressed at a temperature of 20°C. Considering only axial deformations, determine the stress in the aluminum shell when the temperature reaches 180°C. 5. In many situations physical constraints prevent strain from occurring in a given direction, for example ε z = 0 in the case shown, where longitudinal movement of the long prism is prevented at every point. Plane sections perpendicular to the longitudinal axis remain plane and the same distance apart. Show that for this situation, which is known as plane strain , we can express σ z , ε x , and ε y as follows: ± ² ³´ µ ¶ · ¸ ¹ µ ² º » ¼´º ½ ³ ¾ ¸ µ ½ ³´º ¶ ³¸ · ¿ ¹ · ² º » ¼´º ½ ³ ¾ ¸ · ½ ³´º ¶ ³¸ µ ¿...
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