please complete the calcs
Sorry about that, here are the complete calculations:
1. Determine the maximum bending moment: M = (w x l^2) / 8, where M is maximum bending moment in foot-pounds, w is the load per linear foot, and l is the span in feet.
M = (360 x 18^2) / 8 = 145,800 ft-lbs
2. Determine the modulus of elasticity for #2 yellow pine: Let's assume the modulus of elasticity for #2 yellow pine is 1,700,000 psi.
3. Calculate the section modulus required for the wood beam:
S = M / (E x c), where S is the section modulus in cubic inches, E is the modulus of elasticity, and c is the distance from the neutral axis to the top or bottom of the wood beam's cross section.
For a simple span, the section modulus required for a rectangular wood beam is:
S = (5wL^4)/(384EI), where w is the load per linear foot, L is the span in feet, E is the modulus of elasticity, and I is the moment of inertia of the beam's cross-sectional area.
I = bd^3/12, where b is the width of the wood beam and d is its depth.
S = (5 x 360 x 18^4) / (384 x 1,700,000 x 0.4) = 0.127 cubic feet
4. Choose a standard size for the wood beam based on its section modulus:
For a beam depth of 10 inches, a recommended width for #2 yellow pine to achieve a section modulus of 0.127 cubic feet would be 6.74 inches.
Therefore, a possible beam size could be 6.74 inches wide by 10 inches deep.
To calculate the deflection at maximum load, we can use the beam deflection formula:
δ = (5wl^4) / (384EI), where δ is the deflection at center of the beam, w is the load per linear foot, l is the span, E is the modulus of elasticity, and I is the moment of inertia of the beam's cross-sectional area.
Plugging in the values, we get:
δ = (5 x 360 x 18^4) / (384 x 1700000 x 0.4 x 6.74 x 10^3)
δ = 1.36 inches (approximately)
Therefore, the expected deflection at maximum load would be approximately 1.36 inches.