200_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

200_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: Sec_2.6.qxd 9/25/08 194 11:40 AM Page 194 CHAPTER 2 Axially Loaded Members or sx (a) DETERMINE ANGLE |tu| sin u cosu 3.0 MPa sin u cosu FOR LARGEST LOAD Point A gives the largest value of x and hence the largest load. To determine the angle corresponding to point A, we equate Eqs. (1) and (2). (2) GRAPH OF EQS. (1) AND (2) 3.0 MPa sin u cos u 5.0 MPa 2 cos u 3.0 5.0 tan u u 30.96° ; (b) DETERMINE THE MAXIMUM LOAD From Eq. (1) or Eq. (2): sx Pmax 3.0 MPa sin u cos u 5.0 MPa 2 cos u xA (6.80 MPa)(225 mm2) ; 1.53 kN Problem 2.6-19 A nonprismatic bar 1–2–3 of rectangular cross section (cross sectional area A) and two materials is held snugly (but without any initial stress) between rigid supports (see figure). The allowable stresses in compression and in shear are specified as a and a, respectively. Use the following numerical data: (Data: ; b1 4b2/3 b; A1 2A2 A; E1 3E2/4 E; 1 5 2/4 4 a2/3 , a1 2 a1/5, a2 3 a2/5; let a 11 ksi, a1 a 6.5 10-6/°F; P 12 kips, A 6 in.2, b 8 in. E 30,000 ksi, 3 5 2/3 490 lb/ft ) 1 (a) If load P is applied at joint 2 as shown, find an expression for the maximum permissible temperature rise Tmax so that the allowable stresses are not to be exceeded at either location A or B. (b) If load P is removed and the bar is now rotated to a vertical position where it hangs under its own weight (load intensity w1 in segment 1–2 and w2 in segment 2–3), find an expression for the maximum permissible temperature rise Tmax so that the allowable stresses are not exceeded at either location 1 or 3. Locations 1 and 3 are each a short distance from the supports at 1 and 3 respectively. 6.80 MPa b1 b2 1 2 P A B E2, A2, a2 E1, A1, a1 (a) R1 1 W1 w1 = — b1 E1, A1, b1 2 W2 w2 = — b2 E2, A2, b2 3 R3 (b) 3 ...
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This note was uploaded on 12/22/2011 for the course MEEG 310 taught by Professor Staff during the Fall '11 term at University of Delaware.

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