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
Question
Book Icon
Chapter 6, Problem 1P
To determine

Calculate the reaction forces at the supports.

Calculate the magnitude of cable sag at joints B and E.

Calculate the tension force in every segment of cable and total length of the cable.

Expert Solution & Answer
Check Mark

Answer to Problem 1P

The vertical reaction at A and F is Ay=60k_ and Fy=60k_ respectively and the horizontal reaction is H=75k_.

The magnitude of cable sag at joint B and E is hB=16ft_ and hE=16ft_ respectively.

The tension force in the cable segment AB and EF is 96k_.

The tension force in the cable segment BC and DE is 80.7k_.

The tension force in the cable segment CD is 75k_.

The total length of the cable is 114.3ft_.

Explanation of Solution

Given information:

The cable supporting concentrated load as shown in given Figure P6.1.

Assumption:

Apply the sign convention for calculating the equations of equilibrium as below.

  • For the horizontal forces equilibrium condition, take the force acting towards right side as positive (+) and the force acting towards left side as negative ().
  • For the vertical forces equilibrium condition, take the upward force as positive (+) and downward force as negative ().
  • For moment equilibrium condition, take the clockwise moment as positive and counter clockwise moment as negative.

Calculation:

Draw the free body diagram as shown in Figure 1.

Fundamentals of Structural Analysis, Chapter 6, Problem 1P , additional homework tip  1

Calculate the support reactions.

Take moment about F.

M=0(Ay×100)(30×80)(30×60)(30×40)(30×20)=0100Ay=2400+1800+1200+600Ay=60k

Calculate the vertical reaction at F.

Ay+Fy=(4×30k)60+Fy=120kFy=60k

Therefore, the vertical support reaction at A and F is Ay=60k_ and Fy=60k_ respectively.

Find the horizontal reaction using general cable theorem.

Take moment about C from support A.

(Ay×40)(H×24)(30×20)=0(60×40)(H×24)(30×20)=024H=1,800kH=75k

Therefore, the horizontal support reaction is H=75k_.

Calculate the magnitude of cable sag at B.

Consider the vertical distance at B is hB.

Take moment at B from support A.

(Ay×20)(H×hB)=0(60×20)(75×hB)=0hB=16ft

Calculate the magnitude of cable sag at E.

Consider the vertical distance at E is hE.

Take moment at E from support F.

(Fy×20)+(H×hE)=0(60×20)+(75×hE)=0hE=16ft

Therefore, the magnitude of cable sag at joint B and E is hB=16ft_ and hE=16ft_ respectively.

Calculate the tension force in the segment of cable AB (TAB) and EF (TEF).

Take joint A as shown in Figure 2.

Fundamentals of Structural Analysis, Chapter 6, Problem 1P , additional homework tip  2

Find the horizontal angle for TAB as follows:

tanθ=16ft20ftθ=38.65°

Apply horizontal equilibrium Equation.

H=0TABcos38.65°75k=0TAB=96k

The cable with supports are symmetrical about vertical axis. Hence, the tension force in the segment AB is equal to EF. So, TEF=96k

Therefore, the tension force in the cable segment AB and EF is 96k_.

Calculate the tension force in the segment of cable BC (TBC) and DE (TDE)

Take joint B as shown in Figure 3.

Fundamentals of Structural Analysis, Chapter 6, Problem 1P , additional homework tip  3

Find the horizontal angle for TBC as follows:

tanθ=8ft20ftθ=21.80°

Apply horizontal equilibrium Equation.

H=0TBCcos21.80°TABcos38.65=0TBCcos21.80°=96cos38.65TBC=80.7k

The cable with supports are symmetrical about vertical axis. Hence, the tension force in the segment BC is equal to DE. So, TDE=80.7k.

The tension force in the cable segment BC and DE is 80.7k_.

Calculate the tension force in the segment of cable CD (TCD).

Take the joint C as shown in Figure 4.

Fundamentals of Structural Analysis, Chapter 6, Problem 1P , additional homework tip  4

Apply horizontal equilibrium Equation.

H=0TCDTBCcos21.80°=0TCD80.7cos21.80°=0TCD=75k

Therefore, the tension force in the cable segments CD is 75k_.

Show the vertical and horizontal length of each segment of cable as shown in Figure 5.

Fundamentals of Structural Analysis, Chapter 6, Problem 1P , additional homework tip  5

Calculate the total length of the cable (L) using Figure 4.

L=LAB+LBC+LCD+LDE+LEF=202+162+202+82+20+202+82+202+162=114.3ft

Therefore, the total length of the cable is 114.3ft_.

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!
Students have asked these similar questions
A) # of Disinfection Clearwells: 3 B) Clearwell Operation Style: Parallel (to provide contact time for disinfection using free chlorine (derived from a hypochlorite solution generated onsite). C) The facility's existing system to generate hypochlorite onsite has reached the end of its useful life, and the current operating capacity is insufficient to generate the required mass flow of hypochlorite to accommodate the future capacity of 34.5 MGD. Assume the facility plans to stop generating hypochlorite onsite and will instead purchase a bulk solution of sodium hypochlorite D) Sodium hypochlorite (NaOCI) concentration: 6.25% NaOCI by mass E) Bulk Density: 1,100 kg/m^3 F) Clearwell T10/DT Ratio: (CW1 0.43). (CW2 = 0.51), (CW3 = 0.58) DT is the theoretical mean hydraulic retention time (V/Q) G) pH: 7.0 H) Design Temperature: 15°C 1) 50% of Chlorine is lost in each clearwell J) If the concentration going into the clearwell is C, then you can assume that the concentration leaving the…
Please explain step by step, and show formula
Note: Please deliver a clear, step-by-step simplified handwritten solution (without any explanations) that is entirely manually produced without AI assistance. I expect an expert-level answer, and I will evaluate and rate it based on the quality and accuracy of the work, using the provided image for additional reference. Ensure every detail is thoroughly checked for correctness before submission.
Knowledge Booster
Background pattern image
Similar questions
SEE MORE QUESTIONS
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