Explanation Given information: Magnitude of the uniformly varying load is 0 ≤ w ≤ 0.8 kip/ft . Magnitude of Force applied at the end is F = 1.5 kip . Length of the beam A B is l A B = 9 ft . Length of the beam B C is l B C = 9 ft . Width of the rectangular cross-section is b = 6 in . Height of the rectangular cross-section is h = 12 in . Modulus of elasticity of a wooden beam is E = 1.6 × 10 3 ksi . For the beam to be in equilibrium. ∑ F y = 0 R A − 1 2 × l A B × w max + R B − F = 0 R A + R B = 1 2 × l A B × w max + F R A + R B = 1 2 × 9 ft × 0.8 kip/ft + 1.5 kip R A + R B = 5.1 kip .................. 1 For the beam to be in equilibrium. ∑ M A = 0 1 2 × l A B × w max × 2 3 l A B − R B × l A B + F × l A C = 0 1 2 × 9 ft × 0.8 kip/ft × 2 3 × 9 ft + 1.5 kip × 18 ft = R B × 9 ft R B = 48.6 kip-ft 9 ft R B = 5.4 kip .......................... 2 From (1) and (2). R A + 5.4 kip = 5.1 kip R A = − 0.3 kip Bending moment Equation is given by M I = E R 1 R = d 2 y d x 2 M I = E d 2 y d x 2 d 2 y d x 2 = M E I Bending moment at section X-X is given by using the Macauley equation. M x = R A x − 0 − 1 2 × x − 0 × w max x − 0 l A B × 1 3 × x − 0 + R B x − l A B + 1 2 × l A B × w max × x − 2 3 × l A B = − 0.3 x − 0 kip − 1 6 × 0.8 kip x − 0 3 9 ft + 5.4 kip x − 9 ft − 1 2 × 9 ft × 0.8 kip × x − 2 3 × 9 ft = − 0.3 x − 0.0148 x 3 + 5.4 x − 9 − 3.6 × x − 6 kip-ft Moment of inertia of the wooden beam is given by I = b h 3 12 = 6 in × 12 3 in 3 12 = 864 in 4 Calculation: Bending moment Equation is given by d 2 y d x 2 = M E I = 1 E I − 0

11th Edition

ISBN: 9780137605460

Author: Russell C. Hibbeler

Publisher: Pearson Education (US)

See similar textbooks

Question

Chapter 12.3, Problem 48P

To determine

The equation of elastic curve and deflection at C .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 12.3, Problem 47P

Chapter 12.3, Problem 49P

Students have asked these similar questions

The beam is subjected to the load shown. Determine the equation of the elastic curve. EI is constant.

For the beam loaded as shown, determine the deflection 6 ft from the wall. Use E = 1.5 x 106 psi and I = 40 in.* 80 lb/ft B 8 ft

Show the detailed solution.

Chapter 12 Solutions

Mechanics of Materials

Ch. 12.2 - Determine the slope and deflection of end A of the...Ch. 12.2 - Determine the slope and deflection of end A of the...Ch. 12.2 - Determine the slope of end A of the cantilevered...Ch. 12.2 - Determine the maximum deflection of the simply...Ch. 12.2 - Determine the maximum deflection of the simply...Ch. 12.2 - Determine the slope of the simply supported beam...Ch. 12.2 - An L2 steel strap having a thickness of 0.125 in....Ch. 12.2 - The L2 steel blade of the band saw wraps around...Ch. 12.2 - A picture is taken of a man performing a pole...Ch. 12.2 - A torque wrench is used to tighten the nut on a...

Knowledge Booster

Similar questions

SEE MORE QUESTIONS

Recommended textbooks for you

Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY