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In many situations it is known that the normal stress in a given direction is zero. For example, ϭz = 0 in the case of the thin plate shown. For this case, which is known as plane stress, show that If the strains ∈x and ∈y have been determined experimentally, we can express ϭx, ϭy and ∈z as follows:
Fig. P2.73
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Mechanics of Materials, 7th Edition
- A rectangular aluminum plate of uniform thickness has a strain gauge at the center. It is placed in a test rig which can apply a biaxial force system along the edges of the plate as shown below. If the measured strains are +0.0005 and +0.001 in the x and y directions respectively, a) Determine the corresponding stresses set up in the plate and the strain through the thickness, εz. Take E=72 GPa and ν=0.32. b) Construct the Mohr’s circle for the loaded plate. c) State the values of the principal stresses. d) Determine the maximum shearing stresses and the directions of the planes on which they occur.arrow_forwardA 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 Xarrow_forwardThe state of in-plane stress at a point on an element of material is shown. Let |σx| = 370 MPa, |σy| = 130 MPa, and |τxy| = 85.0 MPa. Use this information to represent the state of stress of the same point that is rotated through an angle of θ = 25.0.arrow_forward
- 4. For a state of biaxial strain (ε biax) in a linear-elastic isotropic material, what are the corresponding stresses? How would this change if the Poisson's ratio was zero? Briefly explain why. Assume standard material constants E, v, λ, etc. Γε Ebiax=0 01 bod 000 0 LO 0 0arrow_forwardIn many situations it is known that the normal stress in a given direc-tion is zero. For example, σz= 0 in the case of the thin plate shown. For this case, which is known as plane stress, show that if the strains εx and εy have been determined experimentally, we can express σx, σyand εz as follows:arrow_forwardThe material is subjected to biaxial loading producing uniform normal stress x and y as shown. The strains are Strainx=−0.00065 and Strainy=−0.00040. Use E=30×106 psi and v=0.30. Determine the following: (a) stress at x. Indicate tension or compression. Use 2 decimal places. (b) stress at y. Indicate tension or compression. Use 2 decimal places. (c) Change in the thickness of the material. Indicate elongation or contraction. Use 5 decimal places and scientific notation of ×10−3(Example: _ . _ _ _ _ _ ×10−3)arrow_forward
- The force applied at the handle of the rigid lever causes the lever to rotate clockwise about the pin B through an angle of 1.6°. The wires are unstretched when the lever is in the horizontal position. (Figure 1) Figure A 200 mm G ,200 mm 300 mm- -H C FY 200 mm 300 mm D E 1 of 1 Part A Determine the average normal strain developed in wire AH. Express your answer using three significant figures. ΠΑΣΦ Τ (EAH) avg= Submit Part B (ECC) avg= Determine the average normal strain developed in wire CG. Express your answer using three significant figures. Submit Part C Request Answer (EDP) avg= vec • VAΣo↓ vec ΠΙΑΣΦΑ Request Answer 4 Determine the average normal strain developed in wire DF. Express your answer using three significant figures. ΠΑΣΦΑ vec ↑ ? ? ? mm/mm mm/mm mm/mmarrow_forward2arrow_forward. The normal stresses at a point in a steel member are δx = 8 ksi, δy = -4 ksi and δz = 10 ksi. Using E = 29 x 103 ksi and v = 0.3, determine the normal strains at this point.arrow_forward
- (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.arrow_forward1- Consider a 50 mm × 50 mm × 50 mm element of graphite-reinforced material with its fibersoriented at 45◦ and constrained against deformation in the x direction. The element isheated 50◦C. What is the stress σx required to enforce this constraint and what are the strainsεy, γxy, and εz?2- Consider a 45° off-axis tensile test coupon. Three strain gages attached as shown beloware reading ε1 = 0.00647, ε2 = −0.00324, and ε3 = 0.008095 at stress level of σx =100 MPa.Determine the off-axis modulus of elasticity Ex the off-axis major Poisson’s ratio ??? andcoefficient of mutual influence of the second kind ???,?.arrow_forwardplease solve with all stepsarrow_forward
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