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 13P
Textbook Problem
229 views

Draw the influence lines for the vertical reactions at supports A and E and the reaction moment at support E of the beam shown in Fig. P8.13.

Chapter 8, Problem 13P, Draw the influence lines for the vertical reactions at supports A and E and the reaction moment at

FIG. P8.13, P8.14, P8.15

To determine

Draw the influence lines for the vertical reactions at supports A and E.

Draw the influence lines for the reaction moment at supportE.

Explanation of Solution

Calculation:

Use Muller-Breslau's principle.

Remove the roller support at A from the given beam and apply a small displacement Δ. Due to the displacement, the structure released in which the deflected shape of the released structure of the beam is drawn.

Sketch the deflected shape of the released structure when the roller support A is removed as shown in Figure 1.

The shape of the influence line is the same as the deflected shape of the released structure.

Sketch the general shape of the influence line for vertical reaction (Ay) at supports A as shown in Figure 2.

Find the influence line ordinate (AA) at A.

Apply 1 kN unit load at point A.

Find the numerical value of the influence-line ordinate at A.

Generally the influence line ordinate (AA’) at A is 1 kN/kN when 1 kN load is placed at A. The value of influence line ordinate in the different points on the beam determined by geometry (similar triangle) of the influence line

Therefore, the influence line ordinate is 1 kN/kN at A.

Refer Figure 2.

Find the influence line ordinate at B using similar triangle.

BBBC=AAACBB6=112BB=12

Similarly calculate the influence line ordinate for Ay in different points on beam and summarize the values as in Table 1.

x (m)PointsInfluence line ordinate of Ay(kN/kN)
0A1
6B12
12C0
15D0
18E0

Sketch the influence line diagram for the vertical reactions at supports A using Table 1 as shown in Figure 3.

Replace the fixed support at E by a roller that prevents the rotation and displacement along horizontal but not in displacement along vertical.

Sketch the deflected shape of the released structure when the fixed support replaced by roller as shown in Figure 4.

The shape of the influence line is the same as the deflected shape of the released structure.

Sketch the general shape of the influence line for vertical reaction (Ey) at supports E as shown in Figure 5.

Apply 1 kN unit load at point E.

Find the influence line ordinate (EE) for Ey at E.

Generally the influence line ordinate (EE’) at E is 1 kN/kN when 1 kN load is placed at E. The value of influence line ordinate in the different points on the beam determined by geometry (similar triangle) of the influence line.

Find the influence line ordinate (CC) for Ey at C.

The value of influence line ordinate for Ey at C and E are equal.

Hence, the influence line ordinate (CC) for Ey at C is 1 kN/kN.

Similarly calculate the influence line ordinate for Ey in different points on beam and summarize the values as in Table 2

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
VocabularyAs a well-educated engineer and intelligent citizen, it is important for you to understand that you n...

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

Why are special fuel injectors needed for GDI systems?

Automotive Technology: A Systems Approach (MindTap Course List)

What is a project plan? List what a project plan can accomplish.

Principles of Information Security (MindTap Course List)

What semi-precision tool is used to take angular measurements?

Precision Machining Technology (MindTap Course List)

List categories of items stored in memory. Explain how manufacturers state memory size.

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

Define SQL data services and list their advantages.

Database Systems: Design, Implementation, & Management

Why are arc strikes outside the welding zone considered a problem on pipe?

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)