Consider a cantilever beam that is 10 ft long and supports a concentrated load o

Question

Consider a cantilever beam that is 10 ft long and supports a concentrated load of 833 lbs at its free end. Assume the beam is 2" x 10" in cross section. Calculate the bending stress distribution that is present at the base of the cantilever and at every 2.5 ft increment toward the free end of the eam ( total of five locations). Indicate numerical values for max. Bending stress at each section. Do a similar excersize for shear stresses at each section.

Please do 6.6 as well: assume the beam is simply supported at either end and carries a uniformly distributed load of 200 lb/ft......

MAX POINTS OFFERED!!!

Explanation / Answer

I = bd^3 /12 = (2/12)*(10/12)^3 /12 = 0.008 ft^4

At base of beam:

moment M = P*L = 833*10 = 8330 lb-ft

Bending stress s = My / I = 8330 *y / 0.008 / 12^2 psi = 7197.12*y psi

At 2.5 ft from base:

M = 833*(10 - 2.5) = 6247.5 lb-ft

Bending stress s = My / I = 6247.5 *y / 0.008 / 12^2 psi = 5423.18*y psi

At 5 ft from base:

M = 833*(10 - 5) = 4165 lb-ft

Bending stress s = My / I = 4165 *y / 0.008 / 12^2 psi = 3615.5*y psi

At 7.5 ft from base:

M = 833*(10 - 7.5) = 2082.5 lb-ft

Bending stress s = My / I = 2082.5 *y / 0.008 / 12^2 psi = 1807.7*y psi

At 10 ft from base:

M = 833*(10 - 10) = 0 lb-ft

Bending stress s = My / I = 0 *y / 0.008 / 12^2 psi = 0 psi

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.