   # Draw the influence lines for the vertical reactions at supports A , B , and E and the shear at internal hinge D of the frame shown in Fig. P8.19. FIG. P8.19

#### Solutions

Chapter
Section
Chapter 8, Problem 19P
Textbook Problem
412 views

## Draw the influence lines for the vertical reactions at supports A, B, and E and the shear at internal hinge D of the frame shown in Fig. P8.19. FIG. P8.19

To determine

Draw the influence lines for the vertical reactions at support A, B, and E.

Draw the influence line for the shear at internal hinge D.

### Explanation of Solution

Calculation:

Apply a 1 k unit moving load at a distance of x from left end B.

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

Refer Figure 1.

Consider the unit load at a variable position x to the left hinge D. (placed portion BD of the beam 0x<30ft).

Find the vertical support reaction (Ey) at E for portion BD.

Take Moment at hinge D from right end E.

Consider clockwise moment as negative and anticlockwise moment as positive.

ΣMDDE=0Ey(15)=0Ey=0

Consider the unit load at a variable position x to the right hinge D. (Place portion DE of the beam 30ft<x45ft).

Find the vertical support reaction (Ey) at E for portion DE.

Take Moment at hinge D from right end E.

Consider clockwise moment as negative and anticlockwise moment as positive.

ΣMDDE=0Ey(15)1(x30)=015Ey=x30Ey=x152

Thus, the equations of the influence line ordinate for Ey are,

Ey=0, 0x<30ft (1)

Ey=x152, 30ft<x45ft (2)

Find the influence line ordinate of Ey using Equation (1) and (2) and summarize the values in Table 1.

 x (ft) Points Influence line ordinate of Ey (k/k) 0 B 0 15 C 0 30 D 0 45 E 1

Sketch the influence line diagram for vertical reaction at support E as shown in Figure 2.

Refer Figure 1.

Find the equation of influence line ordinate for the vertical reaction (Ay) using equilibrium equation.

Apply moment equilibrium at B.

Consider clockwise moment as negative and anticlockwise moment as positive.

ΣMB=0Ey(45)+Ay(15)1(x)=015Ay=x45EyAy=x153Ey (3)

Find the influence line ordinate of vertical reaction (Ay) for portion BD (0x30ft).

Substitute 0 for Ey in Equation (3).

Ay=x153(0)=x15 (4)

Find the influence line ordinate of vertical reaction (Ay) for portion DE (30ft<x45ft).

Substitute x152 for Ey in Equation (3).

Ay=x153(x152)=x15x5+6=x3x15+6=62x15 (5)

Find the influence line ordinate of Ay using Equation (4) and (5) and summarize the values in Table 2.

 x (ft) Points Influence line ordinate of Ay (k/k) 0 B 0 15 C 1 30 D 2 45 E 0

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

Refer Figure 1.

Find the equation of influence line ordinate for the vertical reaction (By) using force equilibrium equation.

Consider the vertical forces equilibrium condition, take the upward force as positive (+) and downward force as negative ().

ΣFy=0By+Ay+Ey=1By=1AyEy (6)

Find the influence line ordinate of vertical reaction (By) for portion BD (0x<30ft)

### 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

Find more solutions based on key concepts
In order to improve the production time, the supervisor of assembly lines in a manufacturing setting of cellula...

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

Research at least three programs that you can use to back up your computer. Which programs did you research? Wh...

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

What are vulnerabilities? How do you identify them?

Principles of Information Security (MindTap Course List)

Define polymorphism, and provide three examples.

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

Wheel A: 32A60H8V Wheel B: 39C100L6V Which wheel is finer?

Precision Machining Technology (MindTap Course List)

Describe the motion of the electrode in keyhole welding.

Welding: Principles and Applications (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) 