Engineering Fundamentals
Engineering Fundamentals
6th Edition
ISBN: 9780357112144
Author: Saeed Moaveni
Publisher: MISC PUBS
Question
Book Icon
Chapter 18, Problem 1P
To determine

Find the stiffness of each spring and the stiffest spring.

Expert Solution & Answer
Check Mark

Answer to Problem 1P

The stiffness of each spring is kA=2.5Nmm, kB=4Nmm, and kC=1Nmm, the stiffest spring is Spring B.

Explanation of Solution

Formula used:

Formula used to calculate the spring force is,

F=kx (1)

Here,

k is the stiffness factor or spring constant,

x is the deflection.

Calculation:

Refer to figure Problem 18.1 in textbook, the graph with force-deflection relationships for three springs A, B and C are given.

Rearrange equation (1) to find k.

k=Fx (2)

Refer to Figure Problem 18.1 in textbook,

For spring A,

At xA=4mm, FA=10N

For spring B,

At xB=10mm, FB=40N

For spring C,

At xC=10mm, FC=10N

Substitute kA for k, 10N for F, and 4mm for x in equation (2),

kA=10N4mm=2.5Nmm (3)

Substitute kB for k, 40N for F, and 10mm for x in equation (2),

kB=40N10mm=4Nmm (4)

Substitute kC for k, 10N for F, and 10mm for x in equation (2),

kC=10N10mm=1Nmm (5)

Comparing the values in equation (3), (4) and (5), the spring B is the stiffest spring.

Therefore, the stiffness of each spring is kA=2.5Nmm, kB=4Nmm, and kC=1Nmm, the stiffest spring is spring B.

Conclusion:

Thus, the stiffness of each spring is kA=2.5Nmm, kB=4Nmm, and kC=1Nmm, the stiffest spring is spring B.

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
Beam ABD is supported and loaded as shown. The cross-section of the beam is also shown. The modulus of elasticity of the beam is 200 GPa. 6.0 kN/m Cross-section: 330 mm 4.5 kN 8.0 kNm 40 mm 2.5 m 1.5 m 20 mm Set up the discontinuity moment function in terms of x. List all the appropriate boundary conditions. Determine the slope function in terms of x. Determine the deflection function in terms of x. Determine the support reactions. Determine the maximum deflection. 290 mm
Draw the Shear Force Diagram and Bending Moment Diagram for the beam shown in Fig.1. The beam is subjected to an UDL of w=65m. L=4.5m L1= 1.8m.  Assume the support at C is pinned, and A and B are roller supports.  E = 200GPa, I = 250x106 mm4.
Calculate the BMs (bending moments) at all the joints of the beam shown in Fig.1 using the Slope Deflection method. The beam is subjected to an UDL of w=65m. L=4.5m L1= 1.8m.  Assume the support at C is pinned, and A and B are roller supports.  E = 200GPa, I = 250x106 mm4.

Chapter 18 Solutions

Engineering Fundamentals

Knowledge Booster
Background pattern image
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Engineering Fundamentals: An Introduction to Engi...
Civil Engineering
ISBN:9781305084766
Author:Saeed Moaveni
Publisher:Cengage Learning
Text book image
Fundamentals Of Construction Estimating
Civil Engineering
ISBN:9781337399395
Author:Pratt, David J.
Publisher:Cengage,