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 46P
Textbook Problem
8 views

13.46 and 13.47 Determine the reactions and the force in each member of the trusses shown in Figs. P13.46 and P13.47 using the method of consistent deformations.

Chapter 13, Problem 46P, 13.46 and 13.47 Determine the reactions and the force in each member of the trusses shown in Figs.

FIG. P13.46

To determine

Calculate the support reactions and the member forces of the truss using method of consistent deformation.

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 negative and the counter clockwise moment as positive.

Method of joints:

The negative value of force in any member indicates compression (C) and the positive value of force in any member indicates tension (T).

Condition for zero force members:

  1. 1. If only two non-collinear members are connected to a joint that has no external loads or reactions applied to it, then the force in both the members is zero.
  2. 2. If three members, two of which are collinear are connected to a joint that has no external loads or reactions applied to it, then the force in non-collinear member is zero.

Calculation:

Find the degree of indeterminacy of the structure using the equation:

i=m+r2j

Here, m is the number of members, r is the reaction of the truss, and j is the number of joints.

Substitute 15 for m, 2 for r, and 8 for j.

i=15+22(8)=1716=1

Therefore, the degree of indeterminacy of the truss is i=1.

Select the member DG as redundant.

The truss and the loading are symmetric. Hence, only analyze the right half CEGH of the truss.

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

Refer Figure 1,

Find the vertical reactions.

The loading of the truss is symmetric.

Ay=Ey=60+60+602Ay=Ey=90kN

Remove the redundant member DG.

At C, the half of downward vertical load consider to the right half.

Sketch the free body diagram of the portion CEGH as shown in Figure 2.

Refer Figure 2,

Consider the forces in the member due to external load as FO.

Find the length of member EH.

LEH=62+82=10ft

Find the member forces using method of joints.

Consider joint E.

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

ΣFy=0

FEHO(610)+90=00.6FEHO=90FEHO=150kFEHO=150k(C)

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

ΣFx=0

FEHO(810)+FEDO=00.8(150)=FEDOFEDO=120kFEDO=120k(T)

Consider joint D.

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

ΣFy=0

FDHO60=0FDHO=60k(T)

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

ΣFx=0

FDCO+FDEO=0FDCO=120k(T)

Consider joint H.

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

ΣFy=0

FHCO(610)FHEO(610)FHDO=00.6FHCO(150)(0.6)60=00.6FHCO=9060FHCO=50k(T)

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

ΣFx=0

FHGOFHCO(810)+FHEO(810)=0FHGO0

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
Give some examples of Excel financial functions.

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

What are some network communications standards and protocols? (460)

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

What is an information system? What is its purpose?

Database Systems: Design, Implementation, & Management

How has technology changed in recent years? Provide of traditional, evolving and emerging technology.

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

The force system shown can be replaced with a single, equivalent couple CR. Determine CR.

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

True or False? On todays vehicles, an electric fuel pump runs only when the engine is running.

Automotive Technology: A Systems Approach (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)

What protects the molten weld metal from atmospheric contamination in GTAW welding?

Welding: Principles and Applications (MindTap Course List)