02-04ChapGere.0009

# 02-04ChapGere.0009 - 2 63.85 MPa 5 2(120 GPa(17 3 10 2 6 8...

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Problem 2.6-12 A copper bar is held snugly (but without any initial stress) between rigid supports (see figure). The allowable stresses on the inclined plane pq , for which u 5 55°, are specified as 60 MPa in compression and 30 MPa in shear. (a) What is the maximum permissible temperature rise D T if the allowable stresses on plane pq are not to be exceeded? (Assume a 5 17 3 10 2 6 /°C and E 5 120 GPa.) (b) If the temperature increases by the maximum permissible amount, what are the stresses on plane pq ? Solution 2.6-12 Copper bar between rigid supports 130 CHAPTER 2 Axially Loaded Members a 5 17 3 10 2 6 / 8 C E 5 120 GPa Plane pq : u 5 55 8 Allowable stresses on plane pq : s allow 5 60 MPa (Compression) t allow 5 30 MPa (Shear) (a) M AXIMUM PERMISSIBLE TEMPERATURE RISE D T s u 5 s x cos 2 u 2 60 MPa 5 s x (cos 55 8 ) 2 s x 52 182.4 MPa t u 52 s x sin u cos u 30 MPa 52 s x (sin 55 8 )(cos 55 8 ) s x 52 63.85 MPa Shear stress governs. s x 52 63.85 MPa Due to temperature increase D T : s x 52 E a ( D T ) (See Eq. 2-18 in Section 2.5)
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Unformatted text preview: 2 63.85 MPa 5 2 (120 GPa)(17 3 10 2 6 / 8 C)( D T ) (b) S TRESSES ON PLANE pq s x 5 2 63.85 MPa s u 5 s x cos 2 u 5 ( 2 63.85 MPa)(cos 55 8 ) 2 t u 5 2 s x sin u cos u 5 2 ( 2 63.85 MPa)(sin 55 8 )(cos 55 8 ) 5 30.0 MPa (Counter clockwise) 5 2 21.0 MPa (Compression) ¢ T 5 31.3 8 C q p u Problem 2.6-13 A circular brass bar of diameter d is composed of two segments brazed together on a plane pq making an angle a 5 36° with the axis of the bar (see figure). The allowable stresses in the brass are 13,500 psi in tension and 6500 psi in shear. On the brazed joint, the allowable stresses are 6000 psi in tension and 3000 psi in shear. If the bar must resist a tensile force P 5 6000 lb, what is the minimum required diameter d min of the bar? P P q p d a A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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