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# 2.4-2 - SEGTtON 2.4 statically indeterminate Structures...

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Unformatted text preview: SEGTtON 2.4 statically indeterminate Structures 1251 Problem 2.4-2 A cylindrical assembly consisting of a brass core and an aluminum collar is compressed lava load P (see ﬁgure). The length of the aluminum collar and brass core is 350 mm. the diameter of the cure is 25 mm, and the outside diameter of the collar is 40 mm. Also. the moduli of elasticity ol‘ the aluminum and brass are 72 GPa and 100 GPa, respectively. (a) If the length ol' the assembly decreases by 0.1% when the load 1’ is applied, what is the magnitude ol‘ the load‘.’ (b) What is the maximum permissible load Pm... it“ the allowable stresses in the aluminum and brass are 80 MPa and Ill) MP3. respectively? {Sin;ee.rtiorl.‘ Use the equations derived in Example 2-5.) W PL Err-411 + EIJAII r” or 5 F 7" (EU/Ll“ 11' Ebflb)(1*) Substitute numerical values: £031., "1- 5,5141, 3 (72 GPalt765.S 111ml) +( 1 (1a GPa)(49(}.9 mm?) = 55.135 MN 1‘“ 49.090 MN x 104.23 MN 0.350 P = (104.23 MN')(¥) 330 mm. 21 2 aluminum _ x 104.2 RN <— 5. E brass lb) .L‘tl_l_t;)\\'.-ttiLE LOAD L = 35“ ”‘m a“ = 3011-11311 m, = 120 MPa at = 40 mm I‘l Use Eus. (2-1221 and b) of Example 2-5. ”I" i '25 mm For aluminum: 7T , 1 a PF (T A: = ‘id3 ‘ "l?" r = ~—-————'“ P = E A -1- E A (J) i —l t r1 Earl“ Jr £1344!) u l u (l i1 1!) Eu ‘= ' 5.8 '3 , so a” 16 mm 7 . F” : (Ia4.231~11~n(—1M1") = 115.31LN 1;, : 7: GR: 551,: 11111 (3le 51,, = Tag .7- GPA 2 490.9 mm1 For brass: ,- .. . .. . PE '5 (a) Dir..1u:.-\sl; {.m- 1-1mm H (1' _ 1’7 __ P _. ‘ ‘ «a . , J: 1’)” _ JP ‘ 1, m (En’lu : EIIAD} ~ {5:012}: or 1.211.350 nun) CHAN ‘ Eli-“b Eh 1 Use EL]. (2-13) or Exampl‘ 2-3. P11: (10.1.33 MN)(—i%ﬂ) : [2:11 RN :1 Aluminum gen-ems. an = 1 l6 kN ‘— ...
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