The ratio of the buckling load to the compressive strength if buckling is prevented What is the buckling load if the member is braced against buckling at its midpoint (4ft) on its weak axis only? What is the buckling load if the member is braced against buckling at its midpoint on both its weak and strong axes?

Mechanics of Materials (MindTap Course List)
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Author:Barry J. Goodno, James M. Gere
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Chapter11: Columns
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Please help with D, E, and F.  Thank you

Given: An 8 foot long 2"x4" wood compression member in a truss. Use the actual
dimensions of 1.5" x 3.5". Assume that the end conditions are ideal pins. The modulus of
elasticity of the wood is E=1.6x10°psi. The compressive strength of the wood is 5,400 psi.
Find:
Euler buckling stress =
Euler buckling load
II²E
(L/r)
II²EA
(L/r)²
radius of gyration =
bh³
12
-√
I=.
1.5in
3.5in
Transcribed Image Text:Given: An 8 foot long 2"x4" wood compression member in a truss. Use the actual dimensions of 1.5" x 3.5". Assume that the end conditions are ideal pins. The modulus of elasticity of the wood is E=1.6x10°psi. The compressive strength of the wood is 5,400 psi. Find: Euler buckling stress = Euler buckling load II²E (L/r) II²EA (L/r)² radius of gyration = bh³ 12 -√ I=. 1.5in 3.5in
d. The ratio of the buckling load to the compressive strength if buckling is prevented
e. What is the buckling load if the member is braced against buckling at its midpoint (4ft) on
its weak axis only?
f. What is the buckling load if the member is braced against buckling at its midpoint on both
its weak and strong axes?
Transcribed Image Text:d. The ratio of the buckling load to the compressive strength if buckling is prevented e. What is the buckling load if the member is braced against buckling at its midpoint (4ft) on its weak axis only? f. What is the buckling load if the member is braced against buckling at its midpoint on both its weak and strong axes?
Expert Solution
Step 1

To Find :

The ratio of the buckling load to the compressive strenght if buckling is prevented,

Given :

The modulus of elasticity of the wood is E=1.6×106psi

The compressive strenght of the wood isσc=5400psi

Formula :

The Eular buckling stress =π2ELr2

The radius of gyration is, k=IA

The eular buckling load is =π2EALr2

 

 

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