Determine the change in the volume of a 10 cm diameter copper sphere that is subjected to a hydrostatic pressure of 120 MPa assuming linear elastic behavior up to this stress level. (V=4/3 rTr’) (E= 125 GPa, v = 0.34, Sy = 200 MPa)

Determine the change in the volume of a 10 cm diameter copper sphere that is subjected to a hydrostatic pressure of 120 MPa assuming linear elastic behavior up to this stress level. (V=4/3 rTr’) (E= 125 GPa, v = 0.34, Sy = 200 MPa)

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 7.6.13P: A solid spherical ball of magnesium alloy (E = 6.5 × l0-6 psi, v = 0.35) is lowered into the ocean...

See similar textbooks

Related questions

Q: Determine the equivalent spring stiffness constant of the following spring in series and parallel.…

Q: Q2: A brass bar of length 2.25 m with a square cross section of 90mm on each side is subjected to an…

Q: QUE3 mON 5 A cylindrical pressure vessel has an inner diameter of1.2 m and a thickness of 12 mm.…

A: Given:Inner diameter,d=1.2 m=120 mmThickness,t=12 mm

Q: an acetylene tank consists of a cylindrical body flat at its base and hemisphere at the other end .…

A: Thickness, t=2 mmDiameter, d=250 mmL=1200 mmσper=180 MPaHoop stress/Circumferential stress,…

Q: A stainless-steel thick-walled cylinder with inner and outer radii (b and a) of 225 mm and 350 mm,…

Q: A cylinder which can be considered as a thin-walled shell, is made of steel plate 16 mm thick and is…

A: Part A) Now find the hoop stress due to rotation as follows.

Q: A cylinder is made of steel plate is intended to be used as a container for compressed air. The…

Q: When filled to capacity, the unpressurized storage tank shown contains water to a height of h- 21…

Q: The cross sectional area of the bar ABCD is 535 mm2. F1 = 40 kN, F2 = 25 kN, F3 = 30 kN. F1 F2 F3 B•…

A: As per bartleby guidelines we are allowed to solve only 1st 3 subparts if multiple subparts are…

Q: Q2: A brass bar of length 2.25 m with a square cross section of 90mm on each side is subjected to an…

Q: An open belt drive connected two parallel shafts 1.2 m apart. The driving and driven shafts rotate…

A: Here Given that L=1.2m= distance between driving pulley and driven pulley N1=350 rpm= rotational…

Q: A cylindrical tank of radius 50cm and wall thickness 4.0 mm is subjected to internal pressure of 2.0…

A: GivenRadius of the tank = 50cm = 0.5 mWall thickness = 4 mm = 0.004 mInternal pressure = 2 MPaTo…

Q: The diameter (d) of a solid rod (i.e., with a circular cross-section) is 16 mm and is made from a…

Q: Determine of the internal resistance force of each segment of the bar shown below. and the total…

A: Find the force in bar and total elongation.

Q: A shaft subjected to torsion experiences a pure shear stress t on the surface. The maximum principal…

Q: Determine if the following stress field is a valid solution of a plane elasticity problem assuming…

A: Give data σxx= -6a1x2σyy= 12a1x2σxy= 12a1y2

Q: The three-dimensional state of stress at a point is given by 30 10 -10] [0]= 10 20 MN/m? %3D -10 20…

A: Given:

Q: The stress–strain diagram for a titanium alloy can be approximated by the two straight lines. If a…

A: Given data: Dimensions of the rectangular cross-section of the strut, b = 2 in and h = 3 in So, the…

Q: Determine the torsional shear stress in the shaft section AB and BC. There is a fixed support at C…

Q: At 20°C, there is a gap d = 0.2 mm between the lower end of the bronze bar and the rigid slab…

Q: The three-dimensional state of stress at ap given by 30 10 -10 [0] = 10 20 MN/m? %3D -10 20

A: Given: σ=3010-1010020-10200 MN/m2

Q: The total volume of inherent strain longitudinal direction is Vx = Kq. H

A: we are discussing a theoretical model to determine the volume of inherent strain in longitudinal…

Q: In thin spherical shell, the ratio of radial to circumferential stress is 1 (a) (b) 1 (с) 2 (d) 4

A: Given: Ratio of radial to circumferential stress in thin spherical shell.

Q: A thin polymer plate PQR is deformed such that corner Q is displaced downward a distance L = 0.10…

Q: 1. The circular tube shown in Fig. 1 is subjected to a uniform internal pressure P; and external…

A: 1 2

Q: The principal plane stresses and associated strains in a plane at a point are s1 = 36 ksi, s2 = 16…

A: Given: The values of principal stresses are s1=36 ksi and s2=16 ksi. The values of strains are…

Q: Assuming the stress state in a rotating gas turbine is axisymmetric, how many stress and/or…

A: For completely determine the stress we need two boundary conditions for complete explanation. We…

Q: The aluminum cube (600x600x600 mm) is put inside a hole of a rigid boundary as shown below.…

A: We have to solve The aluminum cube (600x600x600 mm) is put inside a hole of a rigid boundary as…

Q: Find the diameter of the propeller shaft, which has to transmit power of 1.5 kW at 8 Hz without…

Q: In the system shown the ABC bar is subjected to a charge Fz = P (in kN) at the same time as a moment…

A: There are three types of stresses produced by the given loading in the question which are- 1. The…

Q: Show that for an annular rotating disc, the ratio of the maximum hoop stress to maximum radial…

Q: A cylinder is made of steel palte is intended to be used as a container for compressed air. The…

Q: The gap between the aluminum bar AB and the magnesium bar 0.2 m 0.25 m CD is 0.4 mm when the…

Q: The cylinder of a hydraulic ram is 20 cm internal diameter. Determine the thickness required to…

Q: 6 m A cylindrical pressure vessel contains a gas at a pressure of 6.0 MPa. The cylinder, which has…

Q: Determine the change in the volume of a 10 cm diameter copper sphere that is subjected to a…

Q: The heels on a pair of women's shoes have a radius of 5 cm at the bottom. If 30% of the weight of a…

Q: * Your answer is incorrect. The solid circular rod has a cross-sectional area of 410 mm². It is…

A: GivenA=410mm2w=9kN/mP=3kNQ=5kNx=0.5m

Q: F2 (2 Q1) Axial displacement of point C in the system shown on the left is 0.01 cm. Find the maximum…

A: Write the given value using suitable variables. Here ΔlC signifies point C axial displacement, F2…

Q: A spherical gas-storage tank with an inside diameter of 31 ft is being constructed to store gas…

A: Given:d=31 ft =372 inp=204 psiSy=31 ksi =31*103 psiN=3

Q: A 150mm* 50mm* 25mm steel block is subjected to a hydrostatic pressure of 10MPa. The Young's modulus…

A: Given:V=150mm*50mm*25mmP=10 MPaE=100GPaμ=0.1

Q: Before loading the plate, mark a line with the inclination shown. After the load is applied, the…

Q: 3. A 1.40 m long steel circular bar is acted upon by forces as shown in fig below. determine the…

Q: Explain the method of representing the combination of normal and shear stresses acting on any plane…

A: Let us take an incremental stressed element from any member.

Q: Choose correct answer: A mild steel rod of 15mm diameter that is 1.5.m in length is elongated by…

Q: If Poisson's ratio of a material is 0.5, then the elastic modulus for the material is a)three times…

A: Given data: μ=0.5 Need to determine the elastic modulus for the material.

Q: A 12cm x 16cm air compressor is operated with a maximum pressure of 10 kg/cm2. There are5 bolts with…

A: Givendi=12cmdo=16cmP=10kg/cm2n=5σy=64ksi

Q: direction in which the normal stress is zero, direction in which the normal stress is zero, ulate…

Q: Investigate which problem can be solved by the two-dimensional stress distribution 011 = 4x1x2; 012…

A: according to the given details,

Concept explainers

Strain energy

The term strain indicates the variation in an object's length, area, and volume when the object is subjected to an external force. The external force may be of normal, shear, moment, torque, etc. The strain in an object depends on the types of external force and cross-section of the object. Mathematically, the evaluation of strain can be obtained with the help of elastic constants.

Question

Determine the change in the volume of a 10 cm diameter copper sphere that is subjected
to a hydrostatic pressure of 120 MPa assuming linear elastic behavior up to this stress
level. (V=4/3 t r') (E= 125 GPa, v = 0.34, Sy = 200 MPa)

Expert Solution

This question has been solved!

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

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 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 solid spherical ball of magnesium alloy (E = 6.5 × l0-6 psi, v = 0.35) is lowered into the ocean to a depth of 8000 ft. The diameter of the ball is 9.0 in. (a) Determine the decrease ?d in diameter, the decrease, ?V in volume, and the strain energy U of the ball. (b) At what depth will the volume change be equal to 0.0324% of the original volume?
Determine the change in the volume of a 10 cm diameter copper sphere that is subjected to a hydrostatic pressure of 120 MPa assuming linear elastic behavior up to this stress level. (V =4/3 n 13) (E: 125 GPa, v = 0.34, SY = 200 MPa)
mechanics of deformable bodies The cylindrical tank has an outer radius of 1.5m and a wall thickness of 25 mm. If the tank is pressurized to 1.5 MPa, determine the longitudinal stress.
A cylindrical pressure vessel has an inner diameter of 4 ft and a thicknessof 1 2 in. Determine the maximum internal pressure it can sustain so that neither its circumferential nor its longitudinal stress component exceeds 20 ksi. Under the same conditions, what is the maximum internal pressure that a similar-size spherical vessel can sustain?
The three-bar truss in Fig. a is subjected to a horizontal force of 5 kip. If the cross-sectional area of each member is 0.20 in2, determine the horizontal displacement at point B. E = 29(103) ksi.
1. A thin-walled cylinder with a diameter of 20 cm and a wall thickness of 2 mm is filled with gas at a pressure of 2 MPa. Calculate the longitudinal stress, and circumferential stress in the cylinder wall.
an acetylene tank consists of a cylindrical body flat at its base and hemisphere at the other end . the thickness of the metal used in tank is 2mm. the tank has a diameter of 250 mm and 1200 mm long. what is the internal pressure of the tank if the allowable stress of the material is 180MPa a. 3.5 kPa b. 6.8 kPa c. 4.2 kPa d. 5.5 kPa
A cylindrical pressure vessel has an inner diameter of 1.2 m and a thickness of 12mm. Determine the maximum internal pressure it can sustain so that neither itscircumferential nor its longitudinal stress component exceeds 140 MPa. Under thesame conditions, what is the maximum internal pressure that a spherical vessel with a similar inner diameter can sustain?
A 1.5-m-diameter cylindrical tank is formed of 6-mm-thick sheet steel (E = 200 Gpa, ν = 0.3). The maximum shear strain occurring in this tank when the contents pressure is 1 MPa, is:
A cylindrical pressure vessel is fabricated from steel plating that has a thickness of 20 mm. The diameter of the pressure vessel is 450 mm, and its length is 2.0 m. Determine the maximum internal pressure that can be applied if the longitudinal stress is limited to 140 MPa, and the circumferential stress is limited to 60 MPa.
The diameter (d) of a solid rod (i.e., with a circular cross-section) is 16 mm and ismade from a homogeneous material. The length (L) of the rod is 1.75 m andYoung’s Modulus for the material (E) is 250 GPa. When the rod is placed undertension it experiences deformation and a stress (?) of 650 MPa. Calculate thefollowing:(i) Strain energy (U) to 2 decimal places in Joules.(ii) Strain energy per unit volume (U/V) in J/m3.(iii) The change in length ∆L to 2 decimal places in mm.(iv) The strain (?) due to deformation to 2 significant figures
A steel bar of 3 m long and 2500 mm2 in area hangs vertically, which is securely fixed on a collar at its lower end . If a weight of 25 KN falls on the collar from the height of 10 mm , determine the stress induced in the bar. What will be the strain energy stored in the bar? Take E=200 GPa.