A strain gage is mounted to the outer surface of a thin-walled boiler. The boiler has an inside diameter of 1820_mm and a wall thickness of 18 mm, and it is made of stainless steel [E = 179 GPa; v = 0.3]. Determine: (a) the internal pressure in the boiler when the strain gage reads 210 µɛ. (b) the maximum shear strain in the plane of the boiler wall. (c) the absolute maximum shear strain on the outer surface of the boiler. Answers: (a) p = i MPa. (b) Ymax in-plane = i prad. (c) Yabs max prad.

A strain gage is mounted to the outer surface of a thin-walled boiler. The boiler has an inside diameter of 1820_mm and a wall thickness of 18 mm, and it is made of stainless steel [E = 179 GPa; v = 0.3]. Determine: (a) the internal pressure in the boiler when the strain gage reads 210 µɛ. (b) the maximum shear strain in the plane of the boiler wall. (c) the absolute maximum shear strain on the outer surface of the boiler. Answers: (a) p = i MPa. (b) Ymax in-plane = i prad. (c) Yabs max prad.

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 7.7.13P: An clement of material in plane strain (see figure) is subjected to strains ex= 480 × 10-6, Ey= 70 ×...

See similar textbooks

Similar questions

- 7.2-26 The strains on the surface of an experiment al device made of pure aluminum (E = 70 GPa. v = 0.33) and tested in a space shuttle were measured by means of strain gages. The gages were oriented as shown in the figure. and the measured strains were = 1100 X 106, h = 1496 X 10.6, and = 39.44 X l0_. What is the stress o in the x direction?
A thin square plate in biaxial stress is subjected to stresses ?? and ??., as shown in part a of the figure. The width of the plate is h = 12.0 in. Measurements show that the normal strains in the x and v directions are s = 427 × 10-6 and s = 113 × l0-6, respectively. With reference to part b of the figure. which shows a Iwo-dimensional view of the plate. determine the following quantities. (a) The increase .d in the length of diagonal Oil. (b) The change . in the angle between diagonal Oti and the x axis, (c) The shear strain y associated with diagonals Oil and cf(that is. find the decrease in angle ced).
An clement of material in plane strain (see figure) is subjected to strains ex= 480 × 10-6, Ey= 70 × l0-6, and yxy= 420 × l0-6. Determine the following quantities: (a) the strains for an element oriented at an angle 0 = 75°, (b) the principal strains, and (c) the maximum shear strains. Show the results on sketches of properly oriented elements.
Compound axial member ABC has a uniform diameter of d=1.45 in. Segment (1) is an aluminum [E1=10,000 ksi] alloy rod with a length of L1=88 in. Segment (2) is a copper [E2=17,000 ksi] alloy rod with a length of L2=128 in. When axial force P is applied, a strain gage attached to copper segment (2) measures a normal strain of ε2=2200 μin./in. in the longitudinal direction. What is the total elongation of member ABC? answer is in inches
Rigid bar ABCD is supported by two bars. There is no strain in the vertical bars before load P is applied. After load P is applied, the normal strain in bar (2) is measured as -3800 μm/m. Use the dimensions L₁ = 1900 mm, L₂ = 1425.00 mm, a = 190 mm, b = 380 mm, and c=143 mm. Determine: (a) the normal strain in bar (1). (b) the normal strain in bar (1) if there is a A = 1 mm gap in the connection at pin C before the load is applied. (c) the normal strain in bar (1) if there is a A = 1 mm gap in the connection at pin B before the load is applied. L₁ Answer: (a) &₁ = (b) E₁ = A i i (c) E₁ = i 1 1 1 a B (1) b Rigid bar L2 με με με C (2)
A steel thick cylinder of external diameter 150 mm has two strain gauges fixed externally, one along the longitudinal axis and the other at right angles to read the hoop strain. The cylinder is subjected to an internal pressure of 75 MPa and this causes the following strains: (a) hoop gauge: 455 x 106 mm/mm tensile; (b) longitudinal gauge: 124 x 10 mm/mm tensile. Find the internal diameter of the cylinder assuming that Young's modulus for steel is 208 GPa and Poisson's ratio is 0.283.
Compound axial member ABC has a uniform diameter of d = 1.45 in. Segment (1) is an aluminum [E₁ = 10,000 ksi] alloy rod with a length of L₁ = 85 in. Segment (2) is a copper [E₂ = 17,000 ksi] alloy rod with a length of L₂ = 121 in. When axial force P is applied, a strain gage attached to copper segment (2) measures a normal strain of 2 = 1800 μin./in. in the longitudinal direction. What is the total elongation of member ABC? SABC = i eTextbook and Media GO Tutorial Save for Later L Aluminum in. B L₂2 Copper CP Attempts: 0 of 5 used Submit Answer
A steel plate is subjected to a state of plane stress (E = 200 GPa and v = 0.29) of Oxx = 105 MPa, Oyy = -19 MPa and Oyy = 96 MPa. Calculate the axial strain, ɛ77, at this point in the z direction, normal to the plate's surface. Provide your answer in microstrain, pɛ. You do not need to type the units.
A rigid steel bar is supported by three rods, as shown. There is no strain in the rods before the load P is applied. After load P is applied, the normal strain in rod (2) is 1020 μin./in. Assume initial rod lengths of L1 = 148 in. and L2 = 78 in. Determine(a) the normal strain in rods (1).(b) the normal strain in rods (1) if there is a 0.043 in. gap in the connections between the rigid bar and rods (1) at joints A and C before the load is applied.(c) the normal strain in rods (1) if there is a 0.043 in. gap in the connection between the rigid bar and rod (2) at joint B before the load is applied.
The 45° strain rosette shown in figure below is mounted on the surface of a thin shell. The following readings are obtained for each gage: ea, eb, and ec. Note that e, is negative. Determine: • Shear strain yay • Principal strains e1 and e2 • The rotation angle (magnitude and direction) from x-axis to reach the principal orientation. Indicate direction as clockwise or counter-clockwise. epsilon_a = 4.50E-04 epsilon_b = 2.00E-04 epsilon_c = -1.00E-04 y а b 45° 45°
A rigid steel bar is supported by three rods, as shown. There is no strain in the rods before the load Pis applied. After load P is applied, the normal strain in rod (2) is 840 pin./in. Assume initial rod lengths of L1 = 120 in. and L2 = 71 in. Determine (a) the normal strain in rods (1). (b) the normal strain in rods (1) if there is a 0.032 in. gap in the connections between the rigid bar and rods (1) at joints A and C before the load is applied. (c) the normal strain in rods (1) if there is a 0.032 in. gap in the connection between the rigid bar and rod (2) at joint B before the load is applied. (1) (2) Rigid bar Answers: (a) E1 = i pin./in. (b) E1 = pin./in. (c) Ɛ1 = i pin./in.
uniform diameter d= 1.75 in. Segment (1) is an aluminum Ę₁ = 10000 ksi L₁ = 90 in. Segment (2) is a copper Ę₂ = 17000 ksi L₂ = 126 in. When Pis applied, a strain gage attached to copper segment (2) measures a normal strain of &2 = 1700 uin./in. in the longitudinal direction. What is the elongation of segment (1)? Answer in inch rounded-off to 3 decimal places L₁ A (1) Aluminum B L2 (2) Copper