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 5, Problem 42P
To determine

Sketch the shear and moment curves for each member of the frame and draw the deflected shape.

Expert Solution & Answer
Check Mark

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 clockwise moment as positive and the counter clockwise moment as negative.

Calculation:

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

Fundamentals of Structural Analysis, Chapter 5, Problem 42P , additional homework tip  1

Refer to Figure 1.

Use equilibrium equations:

Summation of moments about F is equal to 0.

MF=0Dy×8+Dx×6=0Dx=43Dy        (1)

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

Fundamentals of Structural Analysis, Chapter 5, Problem 42P , additional homework tip  2

Refer to Figure 2.

Use equilibrium equations:

Summation of moments about B is equal to 0.

MB=0Dy×10Dx×6+4×10×102+35×3=0Dy×10(43Dy)×6+4×10×102+35×3=0Dy=16.94kips()

From Equation (1).

Dx=43×16.94=22.59kips()

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

+Fy=0By4×10+16.94=0By=23.06kips()

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

+Fx=0Bx+3522.59=0Bx=12.41kips()

Refer to Figure 1.

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

+Fy=0Fy16.94=0Fy=16.94kips()

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

+Fx=0Fx+22.59=0Fx=22.59kips()

Sketch the free body diagram of the segment AB as shown in Figure 3.

Fundamentals of Structural Analysis, Chapter 5, Problem 42P , additional homework tip  3

Refer to Figure 3.

Use equilibrium equations:

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

+Fy=0Ay23.06=0Ay=23.06kips()

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

+Fx=0Ax+12.41=0Ax=12.41kips()

Summation of moments about A is equal to 0.

MA=012.41×6+MA=0MA=74.46kipsft

Calculate the shear at each point of the frame as shown below.

VA=12.41kipsV@Left of B=12.41kipsV@Left of C=12.4135             =22.59kipsVC=23.06kips

VD=23.064×10    =16.94kipsVE=23.064×10    =16.94kips

V@Right of E=22.59kipsVF=22.5922.59   =0

Maximum bending moment occurs between the member CD.

Consider the shear between CD at a distance x from C is equal to zero.

Vx=023.064×x=0x=5.765ft

Calculate the moment at each point of the frame as shown below.

MA=74.46kipsftMB=74.46+12.41×6=0

M35 kips=74.46+12.41×9=37.23kipsftMC=74.46+12.41×1235×3=30.54kipsft

M5.765ft from C=23.06×5.76530.544×5.765×5.7652                     =35.93kipsftMD=23.06×1030.544×10×102      =0

ME=23.06×1830.544×18×182=135.5kipsftME=135.5+22.59×6=0

Sketch the shear and moment curves of the frame as shown in Figure 4.

Fundamentals of Structural Analysis, Chapter 5, Problem 42P , additional homework tip  4

Sketch the deflected shape of the frame as shown in Figure 5.

Fundamentals of Structural Analysis, Chapter 5, Problem 42P , additional homework tip  5

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