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 8, Problem 37P
Textbook Problem
133 views

Draw the influence lines for the reaction moment at support A, the vertical reactions at supports A and F, and the shear and bending moment at point E of the frame shown in Fig. P8.37.

FIG. P8.37

Chapter 8, Problem 37P, Draw the influence lines for the reaction moment at support A, the vertical reactions at supports A

To determine

Draw the influence lines for the reaction moment at support A, the vertical reactions at supports A and F and the shear and bending moment at point E.

Explanation of Solution

Calculation:

Influence line for moment at support A.

Apply a 1 kN unit moving load at a distance of x from left end C.

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

Refer Figure 1.

Apply 1 kN load just left of C (0x5m).

Take moment at A from B.

Consider clockwise moment as positive and anticlockwise moment as negative.

MA=1(5x)=x5

Apply 1 kN load just right of C and just left of D (5mx10m).

Take moment at A from D.

MA=1(x5)=x5

Apply 1 kN load just right of D and just right of F (10mx20m).

Take moment at A from F.

MA=1(x5)Fy(15)=x515Fy

Thus, the equation of moment at A as follows,

MA=x5, (0x10m) (1)

MA=x515Fy, (10mx20m) (2)

Find the influence line ordinate of MA at B using Equation (1).

Substitute 0 for x in Equation (1).

MA=05=5kN-m

Find the influence line ordinate of MA at F using Equation (2).

The vertical reaction at F is 1 kN when 1 kN applied at F.

Substitute 20 m for x and 1 kN for Fy in Equation (2).

MA=20515(1)=1515=0

Thus, the influence line ordinate of MA at F is 0kN-m/kN.

Similarly calculate the influence line ordinate of MA at various points on the frame and summarize the values in Table 1.

x (m)PointsInfluence line ordinate of MA(kN-m/kN)
0B‑5
5C0
10D5
20F0

Sketch the influence line diagram for the moment at support A using Table 1 as shown in Figure 2.

Influence line for vertical reaction at support F.

Apply a 1 kN unit moving load at a distance of x from left end C.

Refer Figure 1.

Find the vertical support reaction (Fy) at F using equilibrium equation:

Apply 1 kN load just left of D (0x10m).

Consider section DF.

Consider moment equilibrium at point D.

Consider clockwise moment as positive and anticlockwise moment as negative

ΣMD=0Fy(10)=0Fy=0

Apply 1 kN load just right of D (10mx20m).

Consider section DF.

Consider moment equilibrium at point D.

Consider clockwise moment as positive and anticlockwise moment as negative

ΣMD=0Fy(10)+1(x10)=010Fy=x10Fy=x101

Thus, the equation of vertical support reaction at F as follows,

Fy=0, (0x10m) (3)

Fy=x101, (10mx20m) (4)

Find the influence line ordinate of Fy at F using Equation (2).

Substitute 20 for x in Equation (1).

Fy=20101=21=1kN

Thus, the influence line ordinate of Fy at F is 1kN/kN.

Similarly calculate the influence line ordinate of Fy at various points on the frame and summarize the values in Table 2.

x (m)PointsInfluence line ordinate of Fy(kN/kN)
0B0
5C0
10D0
15E0.5
20F1

Sketch the influence line diagram for the vertical reaction at support F using Table 2 as shown in Figure 3.

Influence line for vertical reaction at support A.

Apply a 1 kN unit moving load at a distance of x from left end C.

Refer Figure 1.

Apply vertical equilibrium in the system.

Consider upward force as positive and downward force as negative.

Ay+Fy1=0Ay=1Fy (5)

Find the equation of vertical support reaction (Ay) from B to C (0x10m) using Equation (5).

Substitute 0 for Fy in Equation (5).

Ay=1(0)=1kN

Find the equation of vertical support reaction (Ay) from C to F (10mx20m) using Equation (5).

Substitute x101 for Fy in Equation (5).

Ay=1(x101)=1x10+1=2x10

Thus, the equation of vertical support reaction at A as follows,

Ay=1kN, (0x10m) (6)

Ay=2x10, (10mx20m) (7)

Find the influence line ordinate of Ay at F using Equation (7).

Substitute 20 m for x in Equation (7).

Ay=22010=22=0

Thus, the influence line ordinate of Fy at F is 1kN/kN.

Similarly calculate the influence line ordinate of Ay at various points on the beam and summarize the values in Table 3.

x (m)PointsInfluence line ordinate of Ay(kN/kN)
0B1
5C1
10D1
15E0.5
20F0

Sketch the influence line diagram for the vertical reaction at support A using Table 3 as shown in Figure 4.

Influence line for shear at point E.

Sketch the free body diagram of the section BD as shown in Figure 5.

Refer Figure 5.

Apply equilibrium equation of forces.

Consider upward force as positive (+) and downward force as negative ().

ΣFy=0

AySE1=0SE=Ay1 (8)

Find the equation of shear force at E of portion BD (0x10m)

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 8 Solutions

Structural Analysis
Show all chapter solutions
add
Ch. 8 - Draw the influence lines for the shear and bending...Ch. 8 - Draw the influence lines for the shear and bending...Ch. 8 - Draw the influence lines for the vertical...Ch. 8 - Draw the influence lines for the shear and bending...Ch. 8 - Draw the influence lines for the shear and bending...Ch. 8 - Draw the influence lines for the vertical...Ch. 8 - Draw the influence lines for the vertical...Ch. 8 - Draw the influence lines for the vertical reaction...Ch. 8 - Draw the influence lines for the vertical...Ch. 8 - Draw the influence lines for the vertical...Ch. 8 - Draw the influence lines for the shear and bending...Ch. 8 - Draw the influence lines for the shear and bending...Ch. 8 - Draw the influence lines for the vertical...Ch. 8 - Draw the influence lines for the vertical...Ch. 8 - Draw the influence lines for the shear and bending...Ch. 8 - Draw the influence lines for the shear and bending...Ch. 8 - Draw the influence lines for the reaction moment...Ch. 8 - Draw the influence lines for the shear and bending...Ch. 8 - Draw the influence lines for the reaction moment...Ch. 8 - Draw the influence lines for the shears and...Ch. 8 - Draw the influence lines for the reaction moments...Ch. 8 - Draw the influence lines for the shears and...Ch. 8 - Draw the influence lines for the vertical...Ch. 8 - Draw the influence lines for the shears and...Ch. 8 - 8.35 and 8.36 Draw the influence lines for the...Ch. 8 - 8.35 and 8.36 Draw the influence lines for the...Ch. 8 - Draw the influence lines for the reaction moment...Ch. 8 - Draw the influence lines for the reaction moment...Ch. 8 - Draw the influence lines for the vertical...Ch. 8 - Draw the influence lines for the shear in panel CD...Ch. 8 - Draw the influence lines for the shear in panel DE...Ch. 8 - Draw the influence lines for the shear in panel BC...Ch. 8 - Draw the influence lines for the shear in panel BC...Ch. 8 - Draw the influence line for the shear in panel CD...Ch. 8 - Draw the influence lines for the forces in the...Ch. 8 - Draw the influence lines for the forces in the...Ch. 8 - Draw the influence lines for the forces in the...Ch. 8 - Draw the influence lines for the forces in the...Ch. 8 - Draw the influence lines for the forces in the...Ch. 8 - Draw the influence lines for the forces in the...Ch. 8 - 8.45 through 8.52 Draw the influence lines for the...Ch. 8 - 8.45 through 8.52 Draw the influence lines for the...Ch. 8 - Draw the influence lines for the forces in the...Ch. 8 - 8.53 through 8.57 Draw the influence lines for the...Ch. 8 - 8.53 through 8.57 Draw the influence lines for the...Ch. 8 - Draw the influence lines for the forces in the...Ch. 8 - 8.53 through 8.57 Draw the influence lines for the...Ch. 8 - Draw the influence line for the vertical...Ch. 8 - 8.59 and 8.60 Draw the influence line for the...Ch. 8 - 8.59 and 8.60 Draw the influence line for the...Ch. 8 - Draw the influence line for the vertical...

Additional Engineering Textbook Solutions

Find more solutions based on key concepts
Show solutions add
Why is important to know integral calculus?

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

5. Describe a data dictionary and list the types of information it contains.

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

What tool is used in Oracle to create users?

Database Systems: Design, Implementation, & Management

Briefly describe how a NoSQL database operates.

Fundamentals of Information Systems

What is data independence, and why is it lacking in file systems?

Database Systems: Design, Implementation, & Management

In addition to the reasons mentioned in this exercise, why else might you want to obtain a copy of yourcredit r...

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

Why is a routine maintenance plan important?

Precision Machining Technology (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)