   # 6.14 through 6.17 Use the moment-area method to determine the slopes, and deflections at points B and C of the beam shown. FIG. P6.17, P6.43

#### Solutions

Chapter
Section
Chapter 6, Problem 17P
Textbook Problem
146 views

## 6.14 through 6.17 Use the moment-area method to determine the slopes, and deflections at points B and C of the beam shown.FIG. P6.17, P6.43 To determine

Find the slope θB&θC and deflection ΔB&ΔC at point B and C of the given beam using the moment-area method.

### Explanation of Solution

Given information:

The Young’s modulus (E) is 29,000 ksi.

The moment of inertia (I) is 4,000in.4.

Calculation:

Consider flexural rigidity EI of the beam is constant.

Show the free body diagram of the given beam as in Figure (1).

Refer Figure (1),

Consider upward is positive and downward is negative.

Consider clockwise is negative and counterclowise is positive.

Determine the support reaction at A using the Equation of equilibrium;

MD=0RA×36(50×27)=0RA=1,35036RA=37.5kips

Determine the reaction at support D;

V=0RA+RD=50RD=5037.5RD=12.5kips

Show the reactions of the given beam as in Figure (2).

Refer Figure 2,

Determine the bending moment at A;

MA=(12.5×36)(50×9)=450450=0

Determine the bending moment at B;

MB=37.5×9=337.5kipsft

Determine the bending moment at C;

MC=37.5×18(50×9)=225kipsft

Determine the moment at D;

MD=(37.5×36)(50×27)=1,3501,350=0

Show the M/EI diagram for the given beam as in Figure (3).

Show the elastic curve diagram as in Figure (4).

Refer Figure (3).

Determine the deflection at D using the relation;

Here, b1 is the width of rectangle, h1 is the height of the triangle, b2 is the width of the triangle, and h2 is the height of the triangle.

Substitute 9 ft for b1, 337.5EI for h1, 27 ft for b2, and 337.5EI for h2.

ΔDA=(12×9×337.5EI)(27+13×9)+(12×27×337.5EI)(23×27)=127,575kips-ft3EI

Determine the slope at point A using the relation;

θA=127,575kips-ft3(L)EI

Here, L is the length of the beam.

Substitute 36 ft for L.

θA=127,575kips-ft3(36)EI=3,543.75kips-ft2EI

Determine the slope at point B using the relation;

θB=θAθAB=θA(12×b×h)

Here, b is the width of the triangle and h is the height of the triangle.

Substitute 3,543.75kips-ft2EI for θA, 9.0 ft for b, and 337.5EI for h.

θB=3,543.75kips-ft2EI(12×9.0×337.5EI)=2,025kips-ft2EI

Substitute 29,000 ksi for E and 4,000in.4 for I.

Hence, the slope at B is 0.0025rad_.

Determine the deflection at point B using the relation;

ΔB=LABθAΔBA=LABθA(12×b×h)(13×b)

Here, LAB is the length of portion A and B, ΔBA is the deflection between the point A and B, b is the width of triangle, and h is the height of the triangle.

Substitute 9.0 ft for LAB, 3,543.75kips-ft2EI for θA, 9.0 ft for b, and 337.5EI for h.

ΔB=(9)(3,543

### 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

Find more solutions based on key concepts
For Problem 19.39, determine the probability (assuming normal distribution) that a tire could be used reliably ...

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

What resources can Iris call on to assist her?

Management Of Information Security

Explain the difference between over steer and under steer.

Automotive Technology: A Systems Approach (MindTap Course List)

Identify types of desktop users and explain how each users computer needs may differ.

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

What is the inch equivalent of 1 millimeter?

Precision Machining Technology (MindTap Course List)

Why must metal that has been used before be cleaned prior to welding?

Welding: Principles and Applications (MindTap Course List)

If your motherboard supports ECC DDR3 memory, can you substitute non-ECC DDR3 memory?

A+ Guide to Hardware (Standalone Book) (MindTap Course List) 