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 38P
Textbook Problem
3 views

13.37 through 13.45 Determine the reactions and draw the shear and bending moment diagrams for the structures shown in Figs. P13.37–P13.45 using the method of consistent deformations.

Chapter 13, Problem 38P, 13.37 through 13.45 Determine the reactions and draw the shear and bending moment diagrams for the

FIG.P13.38

To determine

Calculate the support reactions for the given structure using method of consistent deformation.

Sketch the shear and bending moment diagrams for the given structure.

Explanation of Solution

Given information:

The structure is given in the Figure.

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 positive when moment taken from left and the counter clockwise moment as positive when moment taken from right.
  • Consider the positive sign indicates the clockwise moment the negative sign indicates the counterclockwise moment.

Calculation:

Sketch the free body diagram of the beam as shown in Figure 1.

Refer Figure 1.

Find the degree of indeterminacy of the structure:

Degree of determinacy of the beam is equal to the number of unknown reactions minus the number of equilibrium equations.

The beam is supported by 4 support reactions and the number of equilibrium equations is 2.

Therefore, the degree of indeterminacy of the beam is i=2.

Select the vertical reaction By and Dy at the supports B and D as redundant.

Release the support B and D and consider the notation of moments due to external load as MO.

Sketch the free body diagram of primary beam subjected to external loading without support B and D as shown in Figure 2.

Refer Figure 2.

Find the reactions at the supports without considering support B and D using equilibrium equations:

Summation of moments of all forces about E is equal to 0.

ME=0MEO1(10)(102+40)35(30)2(20)(202)=0MEO=1,900k-ft()

Summation of forces along y-direction is equal to 0.

+Fy=0EyO1(10)352(20)=0EyO=85k()

For unit value of the unknown redundant Dy:

Consider the notation of moments due to external load as mD.

Sketch the free body diagram of primary beam Subjected to unit value of redundant Dy as shown in Figure 3.

Refer Figure 3.

Find the support reaction and moment at E when 1 k vertical load applied at B.

Summation of moments of all forces about A is equal to 0.

ME=0MEB=1(40)MEB=40k-ft()

Summation of forces along y-direction is equal to 0.

+Fy=0EyB+1=0EyB=1k()

For unit value of the unknown redundant By:

Consider the notation of moments due to external load as mB.

Sketch the free body diagram of primary beam Subjected to unit value of redundant By as shown in Figure 4.

Refer Figure 4.

Find the support reaction and moment at E when 1 k vertical load applied at D.

Summation of moments of all forces about E is equal to 0.

MD=0MED=1(20)MED=20k-ft()

Summation of forces along y-direction is equal to 0.

+Fy=0EyD+1=0EyD=1k()

Find the moment equation of the beam for different sections on the beam.

Consider a section XX in the portion AB of the primary structure at a distance of x from A.

Refer Figure 1.

Draw the primary structure with section XX as shown in Figure 5.

Refer Figure 5.

Portion AB.

Consider origin as A. (0x10ft).

Find the moment at section XX in the portion AB as shown in Figure 5.

MO=1(x)(x2)=x22

Similarly calculate the moment of the remaining section in the external loading and redundant loading structures.

Tabulate the moment equation of different segment of beam as in Table 1.

Segmentx-coordinateMO (k-ft)mBY (k-ft/k)mDY (k-ft/k)
OriginLimits (ft)
ABA010x2200
BCE10201(10)(x102)1(x10)0
CDG20301(10)(x5)+35(x20)1(x10)0
DED3050[1(10)(x5)+35(x20)+(x30)2]1(x10)1(x30)

The vertical deflection at point B due to external loading is ΔBO, vertical deflection at point D due to external loading is ΔDO,  and the flexibility coefficient representing the deflection at B due to unit value of redundant By is fBB, the redundant Dy is fDD, and the both redundant By and Dy is fBD=fDB.

Calculate the value of ΔBO using the equation as follows:

ΔBO=ΣMOmBYEIdx=1EI{010(x22)(0)dx+1020[1(10)(x102)][1(x10)]dx+2030[1(10)(x5)+35(x20)][1(x10)]dx+3050[1(10)(x5)+35(x20)+(x30)2][1(x10)]dx}=1EI[05,833.3360,000753,333.33]=819,166.67EIk-ft3

Calculate the value of ΔDO using the equation as follows:

ΔDO=ΣMOmDYEIdx=1EI{010(0)dx+1020(0)dx+2030(0)dx+3050[1(10)(x5)+35(x20)+(x30)2][1(x30)]dx}=1EI[0+0+0280,000]=280,000EIk-ft3

Calculate the value of fBB using the equation as follows:

fBB=ΣmBY2EIdx=1EI{010(0)2dx+1020[1(x10)]2dx+2030[1(x10)]2dx+3050[1(x10)]2dx}=1EI[0+333

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
Identify and list at least five different materials that are used in a TV set or computer.

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

Optical character recognition (OCR) and optical mark recognition (OMR) are two technologies used by QR code rea...

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

What would happen to the output of an AC generator if one of the stator windings has an open?

Automotive Technology: A Systems Approach (MindTap Course List)

Describe the agile development process.

Fundamentals of Information Systems

Calculate all forces acting on the bar AB described in Prob. 5.1.

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

How is the go member of a go/no-go ring gage set identified?

Precision Machining Technology (MindTap Course List)

Identify three reasons for increased spending on data centers.

Principles of Information Systems (MindTap Course List)

Why must a mushroomed chisel or hammer be reground?

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)