b) Define volumetric strain. Prove that the volumetric strain fora rectangular bar subjected to an axial load P in the direction of its length is given by: Sl T(1-2v) E Where: v: Poisson's ratio. ev -

b) Define volumetric strain. Prove that the volumetric strain fora rectangular bar subjected to an axial load P in the direction of its length is given by: Sl T(1-2v) E Where: v: Poisson's ratio. ev -

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter7: Analysis Of Stress And Strain

Section: Chapter Questions

Problem 7.7.4P: An element of material in plain strain is subjected to strains x = 0.0015, , y . = -0.0002, and xy =...

See similar textbooks

Related questions

Q: derive the formula for the moment of inertia of a rectangle rotated about the centroidal x-axis Icx…

Q: H.W.9 The two bars shown in Figure P2.2 are used to support load P. When unloaded, joint B has…

Q: - A wholeseller supplies 30 stuffed dolls each d e manufacturer in lots of 120 each at 71200 pe O…

A: given:annual demand D=30×250=7500Ordering cost c0=60+250=310carrying cost ch=0.6+(2%×12)of…

Q: Find the velocity of car Kinetic energy=888 J Mass of car=70 kg

Q: A bar is attached to the spring at the point C. The left end of the bar is pin supported and can…

Q: Compute the pressure at depth of 0.99 m from free surface of water

A: Given data : Depth h=0.99 m Density of water ρ=1000 kg/m3 Acceleration due to gravity g=9.81 m/s2…

Q: What two factors initiate the defrostmode in the diagram?

A: To heat the interior unit, the indoor coil acts as a condenser, and the outdoor coil acts as an…

Q: Determine the heat flow between the roof and floor of 4 × 3 m size of a furnace of 4 m × 4 m × 3m…

Q: ✓ Figure shows a wheel rotating about O₂. Two points A and B located along the radius of wheel have…

Q: In a truss it is assumed that the members are joined by: Select one: O a. smooth pins O b. welding O…

A: In order to avoid the creation of bending strains, this is believed to be the case. Straight parts…

Q: (15) An alloy steel sheet with a central crack was subjected to a uniaxial stress 40,000 psi when…

Q: 1. The position vector po is obtained by a. Coordinates of Q minus coordinates of the origin b.…

Q: The allowable shearing stress is 15 ksi in the steel rod AB and 8 ksi in the brass rod BC. A torque…

A: Given data: τBC=8 ksiT=13 kip.in Need to determine the required diameter of rod BC.

Q: Ambient air enters a cooling coil at 24°C db-temperature and 50% relative humidity with a dry air…

A: Dear student, we are suppose to solve only 3 sub parts. Please post other parts as a separate…

Q: For the truss in the figure below, if P = 7 kN, what is the force in member DC? -3 m-3 m-3 m- F E VP…

A: Given data P=7 kN

Q: The diameter of the wheel (in mm) is

A: Given data, Figure shows a wheel rotating about O2.Two points A and B located along the radius of…

Q: a) What is a truss? Explain shortly in your own words, and illustrate with one example. b) For the…

A: Answer (a): Truss: A fixed frame of members which is used to support something (roof, bridge) is…

Q: Find the potential energy stored in object Mass of object=9.55 kg Height to be raised=3.33 m

A: Given data : Mass of object=m Height to be raised=h Acceleration due to gravity=g Required :…

Q: The hoisting system shown is used to easily raise kayaks for overhead storage. Determine the…

Q: 5. For the truss shown in Figure below, calculate the stresses in members BE, AC, and BC.…

Q: Water is flowing upwards through the venture meter shown in the figure. The water volumetric flow…

A: Givenρw=1ρhg=13.54Q=0.54 m3/s

Q: Which of the following is the rating life for a ball bearing with total expected life of 20 x 106…

Q: 5. For the cross-section below fill in the required values b. Locate the centroid of the cross…

Q: 2.0 Engine oil at 100°C and a velocity of 0.25 m/s flows over both surfaces of a 0.8-m-long flat…

Q: A liquid (S.D. =2.8 is flowing in a 150mm diameter pipe. The total energy at a given point is found…

Q: Table Q1 shows the initial temperature distribution of a 1 cm long steel bar at equal distance Table…

A: Given : Initial Temperature - 110, 85, 70, 55, 17 L = 1 cm Diffusivity, K = 2.5 cm2/s To find : a)…

Q: The 160-lb exerciser is beginning to execute a bicep curl. When in the position shown with his right…

A: Given:m=160lbmc=20lba=0.30g

Q: a) A fluid flow across the xy plane is given with expression of V = (u, v) = (bx + 2cy)i —…

A: Given data V=bx+2cyi-2ax+byj Here, V represents the velocity vector for the given flow field. From…

Q: Machine shaft alignment theory and evaluation A. Theory of shaft alignment B. Evaluation of shaft…

A: intro- shaft alignment are used for transferring of power from one shaft to another shaft.

Q: A pair of spur gears with 20° full-depth involute teeth, the pinion shaft is connected to a 10 kW,…

Q: 40 kW at 40 rev/s, when it is designed he fuel is 44 MJ/kg. If the indicated over consumption. g/MJ…

A: given:power developed P=40kwN=40rev/svolumetric compression ratio 10overall efficiency…

Q: Q3 A translational mechanical system can be simplified in schematic diagram as in (a) Draw the free…

A: Translational Mechanical systems have three basic elements and they are mass, spring, and damper. If…

Q: A chain drive is desired to couple a gearmotor with a bucket elevator. The 40 hp. gearmotor will…

Q: Explain why modern turbofan engines have more than one stage in the core turbine. Your answer should…

Q: Find the potential energy stored in object Mass=8 kg Height to be raised=10 m

Q: Air at p = 1 atm enters a thin-walled (D = 5-mm diameter) long tube (L = 2 m) at an inlet…

Q: Find the density of liquid having specific gravity 1.221

A: Given data : Specific gravity=S.G Density of water=ρW Required : Density of liquid

Q: atch the picture with the correct Miller indices describing the planes shown: 3 a₁ 4 Faz E D E 2₁ a₁…

Q: The graph shown provides the pump characteristics (performance) curves. There are two pumps in the…

A: For given characteristic curves for pump 1 and pump 2, When pumps will be connected in series, their…

Q: Determine the magnitude of the horizontal reaction (N) at A if P = 229 N and Q = 1966 N. Let x =…

Q: Engine oil at 100°C and a velocity of 0.20 m/s flows over both surfaces of a 1.1-m-long flat plate…

Q: Q3 A translational mechanical system can be simplified in schematic diagram as in (a) Draw the free…

A: Given: Let us consider the given figure, To find: The system's free body diagram. The system's…

Q: In the figure, link 2 rotates with constant annular velocity CO2. A slider link 3 moves outwards…

A: Given:Velocity of slider=VQ/PAngular velocity of link=ω2

Q: Given a fourbar linkage with the link lengths L1 - d - 100 mm, L2-a- 50 mm, L3-b-120 mm, L4c-80 mm.…

Q: In an ECM process for machining iron, it is desired to obtain a metal removal rate of 1 cm³/min.…

Q: Sketch two more stress-strain diagrams, again one for a ductile material and one for a brittle…

A: Stress and strain: Stress is defined as the internal resisting force per unit area; it represents…

Q: Using a double-acting cylinder a work piece is removed and tipped onto a conveyor belt. Following…

A: Given: Let us consider the given image,

Q: A ball is dropped from the top of a tower 80ft high. At the same instant, a second ball is thrown…

A: Given data: h=80 ftu2=40 ft/su1=0 ft/sg=32.2 ft/s2 Need to determine the time taken to pass the ball…

Q: Figure 5.15 in the text gives a schematic of a Carnot cycle operating with a H₂O liquid/vapor with a…

Question

b) Define volumetric strain. Prove that the volumetric strain for a rectangular bar subjected to an,
axial load P in the direction of its length is given by:
81
ev = (1-2v)
E
Where: v: Poisson's ratio.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

A brass plate with a modulus of elastici ty E = 16 X 106 psi and Poisson’s ratio a = 0.34 is loaded in biaxial stress by normal stresses r and cry. (sec figure). A strain gage is bonded to the plate at an angle 4 = 350 If the stress o is 10,700 psi and the strain means used by the gageise = 390 X 106.whatisthcmax- imum in-plane shear stress (Tr, ),. and shear strain (>‘ ).? What is the maximum shear strain (y ) in the x-: plane? What is the maximum shear strain (y ).. in the y-r plane?
An element of material in plain strain is subjected to strains x = 0.0015, , y . = -0.0002, and xy = 0.0003. (a) Determine the strains for an element oriented at an angle = 20°. (b) Determine the principal strains of the element. Confirm the solution using Mohr’s circle for plane strain.
A rosette consisting of 3 gages forming, respectively, angles of θa, θb and θc with the x-axis is attached to the free surface of machine components made of material with a given Poisson’s ratio v and Modulus of elasticity E as shown in Fig. 6. Take note that strain values given above are the gage readings and not principal strains. PLEASE ANSWER I,G,H
The length of a wire increases from 1.25 m to 1.2508 m when a load of 12 kg is suspended. The radius of the wire is 0.5 mm. Find the stress, strain and young's modulus of material of the wire. Draw a free body diagram.
A rosette consisting of 3 gages forming, respectively, angles of θa, θb and θc with the x-axis is attached to the free surface of machine components made of material with a given Poisson’s ratio v and Modulus of elasticity E as shown in Fig. 6. Take note that strain values given above are the gage readings and not principal strains.
A metal bar 5.0 m long extends by 0.05 mm when a tensile load is applied to it. The percentage strain is:
9- What strain will be produced by a stress of 40 x 106 N/m2, for a given modulus of elasticity 200GPa. a. 0.0008 b. 0.0002 c. 0.004 d. 0.002
A copper rod with a diameter of 19 mm, modulus of 110 GPa, and a Poisson’s ratio of 0.35 is subjected to tension within the elastic region. Determine the force ( in N) that will produce a reduction of 0.003 mm in the diameter. I The answer is supposed to be 14,063 but im getting something else. Can you show how its supposed to be 14,063
2.Show that volumetric strain in a bar is equal to the sum of strains in three mutually perpendicular directions. 3. Explain the terms: (i) Modulus of elasticity (ii) Modulus of rigidity and (ii) Bulk modulus. 4. Derive the relationship between (i) Modulus of elasticity and modulus of rigidity (ii) Modulus of elasticity and bulk modulus
A steel bar is stressed to 280MPa.The modulus of elasticity is 205 GPa. The bar is 80mm diameter and 240 mm long. Determine the following I) the strain 2) the force
Question 1A rod with a diameter of 30 mm and a length of 600 mm is subjected to an axial force of 60 kN which causes an elongation of 0.30 mm. Determine the stress in the rod, the strain, and the modulus of elasticity of the material.
Determine the natural strain at point B for the given figure,i need correct solution ASAP