BuyFindarrow_forward

Structural Analysis

6th Edition
KASSIMALI + 1 other
Publisher: Cengage,
ISBN: 9781337630931

Solutions

Chapter
Section
BuyFindarrow_forward

Structural Analysis

6th Edition
KASSIMALI + 1 other
Publisher: Cengage,
ISBN: 9781337630931
Chapter 13, Problem 13P
Textbook Problem
842 views

Determine the reactions and draw the shear and bending moment diagrams for the structures shown in Figs. P13.13–P13.25 using the method of consistent deformations.

Chapter 13, Problem 13P, Determine the reactions and draw the shear and bending moment diagrams for the structures shown in

FIG. P13.13

To determine

Find the reactions and sketch the shear and bending moment diagrams for the given beam using method of consistent deformation.

Explanation of Solution

Given information:

Apply the sign conventions for calculating reactions, forces and moments using the three equations of equilibrium as shown below.

  • For summation of forces along x-direction is equal to zero (Fx=0), consider the forces acting towards right side as positive (+) and the forces acting towards left side as negative ().
  • For summation of forces along y-direction is equal to zero (Fy=0), consider the upward force as positive (+) and the downward force as negative ().
  • For summation of moment about a point is equal to zero (Matapoint=0), consider the clockwise moment as negative and the counter clockwise moment as positive.

Calculation:

Show the beam as shown in the Figure 1.

Refer Figure 1.

Consider the horizontal and vertical reaction at A are denoted by Ax and Ay.

Consider the vertical reaction at B and D is denoted by By and Dy.

The reactions acting in the beam is 4.

The number of Equilibrium reaction is 3.

The degree of indeterminacy of the beam is 1.

Take the vertical reaction at B as the redundant.

Modify the Figure 1 as shown in Figure 2.

Refer Figure 2.

Consider a section at a distance x from both the supports A and C.

The deflection at B due to the external loading is denoted by ΔBO.

The flexibility coefficient representing the deflection at B due to unit value of redundant By is fBB.

Primary beam subjected to unit value of redundantBy.

The loading in the beam is symmetrical.

Calculate the value of reaction at A and D as follows:

Ay=Dy=12

Calculate the value of deflection fBB as follows:

fBB=1EI[012(x2)2dx+23012(x2)2dx]=1EI[14012x2dx+16012x2dx]=1EI[14(x33)012+16(x33)012]=1EI[14(12330)+16(12330)]

fBB=1EI[144+96]=240kNm3/kNEI        (1)

Primary beam subjected to external loading.

Take the sum of the moment about A as zero.

MA=025×12×6250×18+Dy×24=0Dy=630024Dy=262.5kN

Take the sum of the forces in the vertical direction as zero.

Fx=0Ay+Dy=25×12+250Ay+Dy=550

Substitute 262.5kN for Dy.

Ay+262.5=550Ay=550262.5Ay=287.5kN

Calculate the value of deflection ΔBO as follows:

ΔBO=1EI[012(287.5x25x22)(x2)dx+2306(262.5x)(x2)dx+23612(262.5x250(x6))(x2)dx]=1EI[12012(287.5x2+25x32)dx1306(262.5x2)dx13612(12.5x2+1,500x)dx]=1EI[12(287.5x33+25x42×4)01213(262.5x33)0613(12.5x33+1,500x22)612]=1EI[12(287

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

Chapter 13 Solutions

Structural Analysis
Show all chapter solutions
add
Ch. 13 - 13.9 through 13.12 Determine the reactions and...Ch. 13 - Determine the reactions and draw the shear and...Ch. 13 - Determine the reactions and draw the shear and...Ch. 13 - 13.13 through 13.25 Determine the reactions and...Ch. 13 - 13.13 through 13.25 Determine the reactions and...Ch. 13 - Determine the reactions and draw the shear and...Ch. 13 - 13.37 through 13.45 Determine the reactions and...Ch. 13 - 13.13 through 13.25 Determine the reactions and...Ch. 13 - 13.13 through 13.25 Determine the reactions and...Ch. 13 - 13.13 through 13.25 Determine the reactions and...Ch. 13 - 13.13 through 13.25 Determine the reactions and...Ch. 13 - 13.13 through 13.25 Determine the reactions and...Ch. 13 - 13.13 through 13.25 Determine the reactions and...Ch. 13 - 13.13 through 13.25 Determine the reactions and...Ch. 13 - 13.13 through 13.25 Determine the reactions and...Ch. 13 - 13.26 through 13.29 Determine the reactions and...Ch. 13 - 13.26 through 13.29 Determine the reactions and...Ch. 13 - 13.26 through 13.29 Determine the reactions and...Ch. 13 - 13.26 through 13.29 Determine the reactions and...Ch. 13 - 13.30 through 13.33 Solve Problems 13.9 through...Ch. 13 - 13.30 through 13.33 Solve Problems 13.9 through...Ch. 13 - 13.30 through 13.33 Solve Problems 13.9 through...Ch. 13 - 13.30 through 13.33 Solve Problems 13.9 through...Ch. 13 - 13.34 through 13.36 Determine the reactions and...Ch. 13 - 13.34 through 13.36 Determine the reactions and...Ch. 13 - 13.34 through 13.36 Determine the reactions and...Ch. 13 - 13.37 through 13.45 Determine the reactions and...Ch. 13 - 13.37 through 13.45 Determine the reactions and...Ch. 13 - 13.37 through 13.45 Determine the reactions and...Ch. 13 - 13.37 through 13.45 Determine the reactions and...Ch. 13 - 13.37 through 13.45 Determine the reactions and...Ch. 13 - 13.37 through 13.45 Determine the reactions and...Ch. 13 - 13.37 through 13.45 Determine the reactions and...Ch. 13 - 13.37 through 13.45 Determine the reactions and...Ch. 13 - 13.46 and 13.47 Determine the reactions and the...Ch. 13 - 13.46 and 13.47 Determine the reactions and the...Ch. 13 - Determine the reactions for the beam shown in Fig....Ch. 13 - Solve Problem 13.1 for the loading shown and a...Ch. 13 - Solve Problem 13.9 for the loading shown in Fig....Ch. 13 - Solve Problem 13.12 for the loading shown in Fig....Ch. 13 - Solve Problem 13.27 for the loading shown in Fig....Ch. 13 - Solve Problem 13.37 for the loading shown in Fig....Ch. 13 - Solve Problem 13.39 for the loading shown in Fig....Ch. 13 - Determine the reactions and the force in each...Ch. 13 - Determine the reactions and the force in each...Ch. 13 - Determine the reactions and the force in each...Ch. 13 - Solve Problem 13.15 by the method of least work....Ch. 13 - Solve Problem 13.16 by the method of least work....Ch. 13 - Solve Problem 13.35 by the method of least work....Ch. 13 - A beam is supported by a fixed support B and a...

Additional Engineering Textbook Solutions

Find more solutions based on key concepts
Show solutions add
VocabularyState the meaning of the following terms: Exponential Function _____ Logarithmic Function _____ Natur...

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

The resultant of the force system shown is a 50-lbft counterclockwise couple. Find P, Q, and C.

International Edition---engineering Mechanics: Statics, 4th Edition

Excessive Phone Heat While using your smartphone, you notice that throughout the day it gets extremely hot, mak...

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

What is the difference between a detail report, a summary report, and an exception report?

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

Describe the common complaints caused by faulty shock absorbers.

Automotive Technology: A Systems Approach (MindTap Course List)

What is the difference between short circuits and open circuits?

Network+ Guide to Networks (MindTap Course List)

List three safety precautions to observe when operating a horizontal band saw.

Precision Machining Technology (MindTap Course List)

What is concurrency control? Why is it important?

Fundamentals of Information Systems

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

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