Fundamentals of Structural Analysis
Fundamentals of Structural Analysis
5th Edition
ISBN: 9780073398006
Author: Kenneth M. Leet Emeritus, Chia-Ming Uang, Joel Lanning
Publisher: McGraw-Hill Education
bartleby

Concept explainers

Question
Book Icon
Chapter 3, Problem 31P

(a)

To determine

Calculate the reactions of the supports.

(a)

Expert Solution
Check Mark

Answer to Problem 31P

The horizontal force at AB is FABx=5.6kips()_.

The vertical force at AB is FABy=5.6kips()_.

The horizontal reaction at C is Cx=25.6kips()_.

The vertical reaction at C is Cy=38.4kips()_.

The horizontal reaction at E is Ex=20kips()_.

The vertical reaction at E is Ey=40kips()_.

Explanation of Solution

Given information:

The structure is given in the Figure.

Apply the sign conventions for calculating reactions 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 counter clockwise moment as positive and the clockwise moment as negative.

Calculation:

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

Fundamentals of Structural Analysis, Chapter 3, Problem 31P , additional homework tip  1

Refer to Figure 1.

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

Fundamentals of Structural Analysis, Chapter 3, Problem 31P , additional homework tip  2

Refer to Figure 2.

Calculate the angle of the member DE as shown below.

tanθ=21θ=63.43°

Use equilibrium equations.

Find the vertical reaction at E:

Summation of moment about B is equal to 0.

MB=0Ey×60+60×40=0Ey=40kips()

Hence, the vertical reaction at E is Ey=40kips()_.

Calculate the horizontal reaction Ex as shown below.

Ex1=Ey2Ex=20kips()

Hence, the horizontal reaction at E is Ex=20kips()_.

Find the horizontal force at B:

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

+Fx=0Bx+20=0Bx=20kips()

Hence, the horizontal force at B is Bx=20kips()_.

Find the vertical force at B:

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

+Fy=0By60+40=0By=20kips()

Hence, the vertical force at B is By=20kips()_.

Sketch the free body diagram of the truss 1 as shown in Figure 2.

Fundamentals of Structural Analysis, Chapter 3, Problem 31P , additional homework tip  3

Refer to Figure 3.

Use equilibrium equations.

Find the horizontal force at AB:

Summation of moments about c is equal to 0.

MC=0FABx×50+20×20+24×2020×30=0FABx=5.6kips()

Hence, the horizontal force at AB is FABx=5.6kips()_.

Calculate the horizontal reaction FABx as shown below.

FABx1=FABy1FABy=5.6kips()

Hence, the vertical force at AB is FABy=5.6kips()_.

Refer to Figure 3.

Use equilibrium equations.

Find the horizontal reaction at C:

Summation of moment about A is equal to 0.

MA=0Cx×50+60×60+24×20+20×6040×100=0Cx=25.6kips()

Hence, the horizontal reaction at C is Cx=25.6kips()_.

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

+Fy=0Cy+5.62460+40=0Cy=38.4kips()

Hence, the vertical reaction at C is Cy=38.4kips()_.

(b)

To determine

Calculate the forces applied to the trusses at joints C, B, and D.

(b)

Expert Solution
Check Mark

Answer to Problem 31P

The horizontal force at B is Bx=20kips()_.

The vertical force at B is By=20kips()_.

The horizontal reaction at C is Cx=25.6kips()_.

The vertical reaction at C is Cy=38.4kips()_.

The horizontal force at D is Ex=20kips()_.

The vertical force at D is Ey=40kips()_.

Explanation of Solution

Given information:

The structure is given in the Figure.

Calculation:

Refer to part (a).

The horizontal force at B is Bx=20kips()_.

The vertical force at B is By=20kips()_.

The horizontal reaction at C is Cx=25.6kips()_.

The vertical reaction at C is Cy=38.4kips()_.

The horizontal force at D is Ex=20kips()_.

The vertical force at D is Ey=40kips()_.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Knowledge Booster
Background pattern image
Civil Engineering
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, civil-engineering and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Text book image
Structural Analysis
Civil Engineering
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:Cengage,
Text book image
Structural Analysis (10th Edition)
Civil Engineering
ISBN:9780134610672
Author:Russell C. Hibbeler
Publisher:PEARSON
Text book image
Principles of Foundation Engineering (MindTap Cou...
Civil Engineering
ISBN:9781337705028
Author:Braja M. Das, Nagaratnam Sivakugan
Publisher:Cengage Learning
Text book image
Fundamentals of Structural Analysis
Civil Engineering
ISBN:9780073398006
Author:Kenneth M. Leet Emeritus, Chia-Ming Uang, Joel Lanning
Publisher:McGraw-Hill Education
Text book image
Sustainable Energy
Civil Engineering
ISBN:9781337551663
Author:DUNLAP, Richard A.
Publisher:Cengage,
Text book image
Traffic and Highway Engineering
Civil Engineering
ISBN:9781305156241
Author:Garber, Nicholas J.
Publisher:Cengage Learning