Chapter 5, Problem 5.8.14P

### Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
ISBN: 9781337093347
Textbook Problem

# A wood beam ABC with simple supports at A and B and an overhang Ã„Chas height h = 300 mm (sec figure). The length of the main span of the beam is L = 3.6 m and the length of the overhang is L/3 = 1,2 m. The beam supports a concentrated load 3P = 18 kN at the midpoint of the main span and a moment PLI2 = 10,8 kN - m at the free end of the overhang. The wood has a weight density y = 5,5 kN/m3. Determine the required width h of the beam based upon an allowable bending stress of 8,2 MPa, Determine the required width based upon an allowable shear stress of 0.7 MPa.

(a)

To determine

Width of the beam.

Explanation

Given Information:

The following figure is given:

â€ƒâ€ƒ

â€ƒâ€ƒL=3.6Â m,Â 3P=18Â kN,Â PL/2=10.8Â kNâ‹…m,Â Î³=5.5Â kN/m3 . The permissible bending stress is 8.2 MPa.

Calculation:

Consider the following diagram:

â€ƒâ€ƒ

The distributed load due to weight density is:

â€ƒâ€ƒq=Î³A=5.5Ã—0.3Ã—bÃ—10âˆ’3Â kN/m

Value of P is 6 kN.

Calculate the upward reaction force at B by taking equilibrium of moments about A as,

â€ƒâ€ƒâˆ‘MA=0â‡’ByL=q(L+L/3)22+3PÃ—L2+PL2â‡’By=q(L+L/3)22L+3P2+P2=q(L+L/3)22L+2P

There is no reaction force in horizontal direction.

Calculate the upward reaction force at A by taking equilibrium of forces in y -direction as:

â€ƒâ€ƒâˆ‘Fy=0â‡’Ay+By=q(L+L/3)+3Pâ‡’Ay=âˆ’By+q(L+L/3)+3Pâ‡’Ay=âˆ’(q(L+L/3)22L+2P)+q(L+L/3)+3Pâ‡’Ay=âˆ’q(L+L/3)22L+q(L+L/3)+P

The bending moment at x is given by:

â€ƒâ€ƒM={Ayxâˆ’qÃ—x22Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â &#

(b)

To determine

Width of the beam

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### What does the term 3 Vs refer to?

Database Systems: Design, Implementation, & Management

#### Explain how flow of traffic is related to density and average speed.

Engineering Fundamentals: An Introduction to Engineering (MindTap Course List)

#### What is risk management, and why is it important? Provide an example.

Systems Analysis and Design (Shelly Cashman Series) (MindTap Course List)

#### List products that contain embedded computers. List the disadvantages of in-vehicle technology.

Enhanced Discovering Computers 2017 (Shelly Cashman Series) (MindTap Course List)