ENGINEERING FUNDAMENTALS
6th Edition
ISBN: 9781337705011
Author: MOAVENI
Publisher: CENGAGE L
expand_more
expand_more
format_list_bulleted
Question
Chapter 18, Problem 23P
To determine
Obtain the expressions for the elastic energy of a linear spring and hard spring.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Question 3 - Strain Transformation
The state of strain at a point in a rectangular block of material using an x-y coordinate system is given by:
• €xx = 51×10-4
€yy = 18 ×10-4
Yxy=-4x10-4
●
●
Part One
a) Which element below best represents the deformed element due to the state of strain in the x-y plane?
6
2
B)
D)
D)
F)
Hint: Consider the relative magnitude and sign of each component of strain
Q4 The beam shown below is made of an alloy of titanium that has a stress-strain diagram that can in part
be approximated by two straight lines. If the material behaviour is the same in both tension and
compression, determine the bending moment that can be applied to the beam that will cause the
material at the top and bottom of the beam to be subjected to a strain of 0.050 mm/mm
3 cm
2 cm
σ(MPa)
1330
1050
σ = 105(10¹) €
σ= 7000€ +980
0.010
gaizu
201
0.050
€ (mm/mm)
2. A tri-metallic bar is uniformly compressed by an axial force P = 40 kN applied
through a rigid end plate as shown in Fig. 2. The bar consists of a circular steel core
surrounded by brass and copper tubes. The steel core has diameter 30 mm, the brass
tube has outer diameter 45 mm, and the copper tube has outer diameter 60 mm. The
corresponding moduli of elasticity are Esteel= 210 GPa, Ebrass= 100 GPa and Ecoper =120
GPa respectively. Calculate the compressive stresses developed osteel , Obrass, and Ocoper
in the steel, brass and copper respectively.
(5)
Copper tube Brass tube
P= 40 kN
-Steel core
30
mm
45
mm
60
mm
Fig. 2
Chapter 18 Solutions
ENGINEERING FUNDAMENTALS
Ch. 18.2 - Prob. 1BYGCh. 18.2 - Prob. 2BYGCh. 18.2 - Prob. 3BYGCh. 18.2 - Prob. 4BYGCh. 18.2 - Prob. BYGVCh. 18.3 - Prob. 1BYGCh. 18.3 - Prob. 2BYGCh. 18.3 - Prob. 3BYGCh. 18.3 - Prob. BYGVCh. 18.4 - Prob. 1BYG
Ch. 18.4 - Prob. 2BYGCh. 18.4 - Prob. 3BYGCh. 18.4 - Prob. 4BYGCh. 18.4 - Prob. BYGVCh. 18.5 - Prob. 1BYGCh. 18.5 - Prob. 2BYGCh. 18.5 - Prob. 3BYGCh. 18.5 - Prob. 4BYGCh. 18.5 - Prob. BYGVCh. 18.6 - Prob. 1BYGCh. 18.6 - Prob. 2BYGCh. 18.6 - Prob. 3BYGCh. 18.6 - Prob. 4BYGCh. 18.6 - Prob. BYGVCh. 18.7 - Prob. 1BYGCh. 18.7 - Prob. 2BYGCh. 18.7 - Prob. BYGVCh. 18 - Prob. 1PCh. 18 - Prob. 2PCh. 18 - Prob. 3PCh. 18 - In Chapter 12, we explained that the electric...Ch. 18 - The deflection of a cantilevered beam supporting...Ch. 18 - Prob. 6PCh. 18 - Prob. 7PCh. 18 - Prob. 8PCh. 18 - Prob. 9PCh. 18 - Prob. 10PCh. 18 - Prob. 11PCh. 18 - Prob. 12PCh. 18 - Prob. 13PCh. 18 - Prob. 14PCh. 18 - A jet plane taking off creates a noise with a...Ch. 18 - Prob. 16PCh. 18 - Prob. 17PCh. 18 - Prob. 18PCh. 18 - Prob. 19PCh. 18 - Prob. 20PCh. 18 - Prob. 21PCh. 18 - Prob. 22PCh. 18 - Prob. 23PCh. 18 - Prob. 24PCh. 18 - Prob. 25PCh. 18 - Prob. 26PCh. 18 - Prob. 27PCh. 18 - Prob. 28PCh. 18 - Prob. 29PCh. 18 - Prob. 30PCh. 18 - Prob. 31PCh. 18 - Prob. 32PCh. 18 - Prob. 33PCh. 18 - Prob. 34PCh. 18 - Prob. 35PCh. 18 - Prob. 36PCh. 18 - Prob. 37PCh. 18 - Prob. 38PCh. 18 - Prob. 39PCh. 18 - Prob. 40PCh. 18 - Prob. 41PCh. 18 - Prob. 42PCh. 18 - Prob. 43PCh. 18 - Prob. 44PCh. 18 - Prob. 45P
Knowledge Booster
Similar questions
- Using Mohr's Circle determine the equivalent state of stress on an element at the same point oriented 60 degrees clockwise with respect to the element shown in the figure below. Suppose that Sigma-x = 151 MPa, Sigma-y= 106 MPa. Determine sigma-x' in MPa. Express your answer to three significant figures. Do not include the units with your answers.arrow_forwardAs seen in the figure, a rigid beam carried by three elastic rods of equal length from points A, B, and C is pulled to Eve from points F by P-force. The modulus of elasticity of the bars are E1=100GPa, E2=120GPa and E3=100GPa. Yield stress σA=40 MPa for bar 1 and 3, yield stress σA=120 MPa for bar number 2. Accordingly, a) determine the load PA that will start the flow, b) the load PG that will cause the migration.arrow_forwardA rigid bar of weight W = 815 Ib hangs from three equally spaced wires-two of steel and one of aluminum (see figure). The diameter of the wires is W = 815 lb What temperature increase AT (in °F) in all three wires will result in the entire load being carried by the steel wires? Before the wires were loaded with W and before the temperature increase AT, all three wires had the same length. (Assume E, = 30 x 106 psi, a. = 6.5 x 10-6/°F, and a = 12 x 10-6/0F.) oFarrow_forward
- A 4-m-long steel plate with a rectangular cross section (10 mm * 50 mm) is resting on a frictionless surface under the sun. The plate temperature is measured to be at 40°C. The plate is then moved into a cold room and is left to rest on a frictionless surface. After several hours, the plate temperature is measured to be at 5°C. The steel has a modulus of elasticity equal to 200,000 MPa and a coefficient of thermal expansion equal to 1.1 * 10-5m/m/°C.a. What is the length of shrinkage?b. What tension load is needed to return the length to the original value of 4 meters?c. What is the longitudinal strain under this load?arrow_forwardMany of the necessities of everyday life, from rubber bands to suspension bridges,depending on the elastic properties of materials. The greater the deforming forces, thegreater the resulting deformation. This proportionality is called Hooke’s law, and theratio of stress to strain is called the elastic modulus. The modulus of elasticity iscalculated by measuring the strain produced.In Figure Q4, a beam is hung by 2 wires namely BD and CE. If a load P on the beam causes the end C to be displaced to 10 mm downward,(a) Label the deformations produced by P on a free-body diagram Find normal strain in wires BD and CE.arrow_forwardThe beam shown in the figure below (Figure 1) is made of steel that has an allowable stress of σallow 14 ksi. Part A Figure く 1 of 1 Determine the largest internal moment the beam can resist if the moment is applied about the z axis. Express your answer to three significant figures. ΕΠΙ ΑΣΦ vec (Mallow) z = Submit Request Answer Part B ? kip.ft Determine the largest internal moment the beam can resist if the moment is applied about the y axis. Express your answer to three significant figures. (Mallow) y = ΕΠΙ ΑΣΦ vec Submit Request Answer 0.25 in 0.25 in. _ E 3 in. 3 in. To.25 in. < Return to Assignment 3 in. 3 in. Provide Feedback ? kip.ftarrow_forward
- The state of stresses at a given point in a material is shown in the figure below together with possible Mohr circle diagrams corresponding to this state of stress. Which of the following circles is correct? 20 N/mm? 10 N/mm? 40 N/mm? 40 N/mm2 10 N/mm? 20 N/mm2 10 20 40 do- to 10 -10+ 10 20 -10+arrow_forward1-A thin aluminum plate profile shown in the accompanying figure is subjected to an axial load. deflection and the average normal stresses along the plate using the model shown in the figure. The plate has a thickness of 0.5 cm and a modulus of Approximate the 2 cm 2 cm elasticity E=70 GPa 2 cm 2 сm 3000 N б ст 6 cm 10 cm 2 cm 2 cmarrow_forwardTwo steel wires support a movable overhead camera weighing W = 110 N as shown in the figure used for close-up viewing of field action at sporting events. At some instant, wire 1 is at an angle a = 20° to the horizontal and wire 2 is at an angle ß = 48°. Both wires have a diameter of 0.76 mm. Determine the tensile stresses in the two wires.arrow_forward
- A tri-metallic bar is uniformly compressed by an axial force P = 40 kN applied through a rigid end plate (see figure). The bar consists of a circular steel core surrounded by a brass and copper tubes. The steel core has a diameter of 30 mm, the brass tube has outer diameter of 45 mm, and the copper tube has outer diameter of 60 mm. the corresponding moduli of elasticity are E, = 210 GPa, E = 100 GPa, and Ec = 120 GPa. Copper tube Brass tube P= 40 kN %3D Steel core 30 mm 45 mm 60 mm Calculate the compressive stress in the steel core in MPa due to the force P. A. 25.1 1. В. 28.3 Calculate the compressive stress in the brass tube in MPa. В. 8.2 С. 22.4 D. 21.8 2. A. 7.9 С. 9.8 D. 10.4 Calculate the compressive stress in the copper tube in MPa. А. 12.5 В. 14.2 С. 16.4 D. 17.8 3.arrow_forwardQuestion 6 An internal stress (temperature stress) will develop if a body is restrained against dimensional change due to temperature change. O True O Falsearrow_forwardThe figure shows a rigid lever arm CBA that is pinned at A and connected to a wire at B. An applied force P causes the lever arm to rotate 0.05 degrees counterclockwise. What is the strain in the wire? P 300 mm C В A -400 mm-arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Structural Analysis (10th Edition)Civil EngineeringISBN:9780134610672Author:Russell C. HibbelerPublisher:PEARSON
Principles of Foundation Engineering (MindTap Cou...Civil EngineeringISBN:9781337705028Author:Braja M. Das, Nagaratnam SivakuganPublisher:Cengage Learning
Fundamentals of Structural AnalysisCivil EngineeringISBN:9780073398006Author:Kenneth M. Leet Emeritus, Chia-Ming Uang, Joel LanningPublisher:McGraw-Hill Education
Traffic and Highway EngineeringCivil EngineeringISBN:9781305156241Author:Garber, Nicholas J.Publisher:Cengage Learning
Structural Analysis (10th Edition)
Civil Engineering
ISBN:9780134610672
Author:Russell C. Hibbeler
Publisher:PEARSON
Principles of Foundation Engineering (MindTap Cou...
Civil Engineering
ISBN:9781337705028
Author:Braja M. Das, Nagaratnam Sivakugan
Publisher:Cengage Learning
Fundamentals of Structural Analysis
Civil Engineering
ISBN:9780073398006
Author:Kenneth M. Leet Emeritus, Chia-Ming Uang, Joel Lanning
Publisher:McGraw-Hill Education
Traffic and Highway Engineering
Civil Engineering
ISBN:9781305156241
Author:Garber, Nicholas J.
Publisher:Cengage Learning