Question 3(a) At point A on the free surface of a loaded aluminum [E = 70 GPa; v = 0.35] component, thestrain rosette shown was used to obtain the following strain data: &α = −300 µ‚ε =735 μ, and ε 410 μ. Determine: (a) the normal stress σx, (b) the normal stress σy, and (c)the shear stress Txy at point A.60°b60°60°x(b) The strain gauge configurations shown below can be used to determine the deflection atthe free end of a cantilever beam by placement of the gauge(s) on the beam as shownfor Case A and Case D, below. The number of each gauge indicate the position it has inthe standard Wheatstone bridge used. Explain why Case D is superior to case A for thisapplication.I TOP2 BOTTOM3 TOP4 BOTTOMCASE ACASED

Answered: Question 3 (a) At point A on the free…

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 7.7.7P: A thin square plate in biaxial stress is subjected to stresses ?? and ??., as shown in part a of the...

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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).
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?
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
The strain components, ex= 940 micro strain, ey= -360 micro strain and yxy=830micro strain are given for a point in body subjected to plane strain. Determine; a. Magnitude of the principal strains b. The direction of the principal strain axes c. The maximum in-plane shear strain. Confirm your answer by means of Mohr's circle of strain and determine the linear strain on an axis inclined at 20 degrees clockwise to the direction of ey
The strain rosette shown below was used to obtain normal strain data at a point on the free surface of a 2024-T4 aluminum alloy machine part. The gage readings were Ea = +630μ, b = +450μ, and Ec = +1200μ. Determine (a) The strain components Ex, Ey, and Yay at the point. (b) The stress components o, y, and Tay at the point. Express the stresses in SI units. (c) The principal stresses and the maximum shearing stress at the point. Gage c Y 90° Gage b Gage a 45° -X
(b) Three strain gauges were arranged in the form of a rectangular rosette and positioned on a test surface, the measured strains were as follows: 81-350 x 10 82-110x 10 E=230 x 10 Determine (1) the principle strains; (1) the principle stresses, the direction of the greater principle strain relative to gauge I. Also draw the Mohr's Strain Cirele. Take the Modulus of Elasticity value to be E-210 GN/m and Poisson's ratio - 0.3.
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
On the free surface of a component, a strain rosette was used to obtain the following normal strain data: €a = 300µɛ, ɛp = 400µs, and Ec = 200µe. Calculate the normal and shear strains in the x-y plane.
Question 2 A 60° strain rosette is installed on the traction-free surface of a component with one of the strain gages aligned along the y-axis, as illustrated in Figure Q2. The gages show the following strain readings upon loading the structure: E, = 925 x10“ ; &, = 740 x10“ ; ɛ. = -555 ×106 (a) Determine the strains in the x-y directions and show the corresponding strain element. (b) Calculate the principal in-plane strains and the corresponding principal directions. Show the principal strain element. (c) Calculate the in-plane maximum shear strain and show the corresponding strain element. (d) If the structure is made of steel with elastic modulus and Poisson's ratio of 220 GPa and 0.30, respectively, calculate the principal stresses. Show the principal stress element. (e) Determine the normal strain in the n-direction. & Ea
The state of strain in a plane element is Ex = -300 x 10-6 , Ey= 450 x 10-6, and Yxy = 275 x 10-6. (a) Use the strain transformation equations to determine the equivalent strain components on an element oriented at an angle of 0 = 30° counterclockwise from the original position. (b) Sketch the deformed element due to these strains within the x-y plane.
I Review The state of strain at the point has components of e, = 230 (10 6), e, = -240 (10 ), and Yay = 500 (10 6). Part A Use the strain-transformation equations to determine the equivalent in-plane strains on an element oriented at an angle of 30 ° counterclockwise from the original position. (Figure 1) Enter your answers numerically separated by commas. AEo 1 vec E, Ey', Yr'y = Figure étv
A 45° strain rosette was placed on the surface of a critical point on an engineering part. The following were measured: Ea = 400 μ C ли 45° mm mm 45° ли Gauge a was aligned with the x-axis. a. Determine Ex, Ey, Yxy b. Using Mohr's Circle, find the principal strains and the maximum shear strain at that point, and find the orientation of the principal planes from the given x-y axes. y ли & = 450 μ ஆ b a mm X mm & c = 500 μ y+ ос mm mm eb 10₂ X

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