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posted by  Engineering power on 10/15/2009 12:39:52 AM  |  status: Closed  |  Earned Karma: 25

2ch

Course Textbook Chapter Problem Needs by
Mechanical Engineering Mechanics of Materials (5th) by Beer, Johnston, DeWolf N/A N/A 10/15/2009 at 11:00:00 PM
Question Details:
Q:Rod BD is made of steel and is used to brace the axially compressed member ABC. The maximum force that can be developed in member BD is 0.02P. If the stress must not exceed 18ksi and the maximum change in length of BD must not exceed 0.0001 times the length of ABC, determine the smallest-diameter rod that can be used for member BD
I don't get the question; why the rod BD will matter if there is no force on x-direction? i want to see the solution and see what can be happen to rod BD when force is only in y-direction
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posted by samuel222 on 10/15/2009 3:47:11 AM  |  status: Live
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posted by PhysicsPhanatic on 10/15/2009 1:06:25 PM  |  status: Live
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Response Details:
FBD = 0.02P = 0.02(130) = 2.6 kips = 2.6 x 103 lb
Now consider the stress:
σ = 18 ksi = 18 x 103 psi
σ = FBD / A ---> A = FBD / σ
                                = 2.6 / 18
                                = 0.14444 in2 --- (Area 1)
Next consider the deformation:
δ = 0.001(144) = 0.144 in
δ = FBDLBD / AE ---> A = FBDLBD / Eδ
                                        = (2.6 x 103)(54) / (29 x 106)(0.144)
                                        = 0.03362 in2 --- (Area 2)
We know that the larger area governs so we use Area 1 to get
A = 0.14444 in2
A = (π/4)d2  ---> d = √[4A / π]
                               = √[4(0.14444) / π]
                               = 0.429 in
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