Problem 12. Two strain gauges a and b are attached to a plate made from a material having a modulus of elasticity of E=70GPa and Poisson's ratio v=0.35. If the gauges give a reading of εa 450(10-6) and ε=100(10-6), determine the intensities of the uniform distributed load wx and Wy acting on the plate. The thickness of the plate is 25 mm. Note: no shear force acts on the plane along the x and y axes Wy
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- 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?3. The elastic portion of the stress-strain diagram for a steel alloy is shown in the figure below. The specimen from which it was obtained had an original diameter of 13 mm and a gauge length of 50 mm. If a load of P = 20 kN is applied to the specimen, determine its diameter and gauge length. Take v = 0.4 σ (MPa) 400 0.002 e(mm/mm)A strain gauge that is attached to the surface of a stressed componentgives 3 readings (εa = 310, εb = B=150, εc = C=-300). If the strain gauge is of the 60 degreestype (indicating the angle between each of the gauges), construct a Mohr’s StrainCircle. Gauge A is aligned along the x-axis. Using Mohr’s Strain Circle calculate the:(i) principal strains (ε1, ε2) (ii) principal angles (φ1, φ2) (You should measure these anticlockwise from the y-axis)(iii) maximum shear strain in the plane (γmax)
- 3Q1 The 45° strain rosette is mounted on a surface of the bracket as shown in Figure Q1. The bracket is made from steel with Esteel = 120 GPa and poison ratio, v = 0.28. The following readings are obtained for each gauge under loadings: Ea= [ 100+20 ] (10-6) Es = -200(10-6) E = -180(10-6) (а) Prove that E= Eaand &y= Ec. (b) Determine the shear strain, y and the normal strain, Ez and Ey. (c) Estimate the in-plane principal strains and the angle associated with the principal strains, andThe strain gauge is placed on the surface of a thin-walled steel boiler as shown The gauge is 0.5 in long and it elongates 0.17(103) in when a pressure is applied. The boiler has a thickness of 0.5 in and inner diameter of 60 in Est = 29(10³) ksi, st = 0.3 (Figure 1) Figure 0.5 in. X 1 of 1 60 in. Determine the pressure in the boiler. Express your answer using three significant figures and include the appropriate units. P = Submit ▾ Part B 0 Value HA Submit Request Answer Ymax in plane Determine the maximum x y in plane shear strain in the material. Express your answer using three significant figures. Units ΑΣΦ | 4 Request Answer ? vec WYCZA ?
- A force P and a force Q, applied via a nut, are acting on the arm attached to the end of a shaft made of steel. The strain gauge readings on point A of the shaft show the following deformation values: ε1 = 630x10-6, ε2 = 600x10-6, and ε3 = - 189x10-6. Determine the magnitudes of the applied forces P and Q (E = 200 GPa, υ = 0.3).Strains measured in a, b and c directions are yardımıa=-150x10-6, ɛb=200x10-6, and ɛc=300x10-6 with the help of the rosette placed at point A of the elastic material under the effect of plane tension. Calculate the principal stresses since the modulus of elasticity in the material is E= 200 GPa and the Poisson ratio ν= 0.3(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.
- The 45° strain rosette is mounted on a surface of the bracket . The bracket is made from steel with Esteel = 120 GPa and poison ratio, v = 0.28. The following readings are obtained for each gauge under loadings:Ɛa = [ X+Y ] (10-6)Ɛb = -200(10-6)Ɛc = -180(10-6) x=100, y=100 (a) Estimate the in-plane principal strains and the angle associated with the principal strains, and (b) Calculate the principal stress associated with the principal strains in (a).The steel (E = 200GPa, v=0.32) vertical post is loaded to the forces as shown in Figure Q1. If the strain gauges a and b are firmly attached at point A give readings of &a=300μ and = 175μ. Determine the magnitudes of P, assuming that P = P2. There is no transverse force occurs at point 4. Solve the following problems: (a) Sketch the free body diagram at point 4, (b) Find the moment of inertia of the cross section, (c) Find the normal strains at point A, and (d) Find force P₁. P₂ A C 2.5 cm 60 cm C Figure Q1 10 cm 2.5 cm Section c-c 5cmThe 45° strain rosette is mounted on a surface of the bracket . The bracket is made from steel with Esteel = 120 GPa and poison ratio, v = 0.28. The following readings are obtained for each gauge under loadings:Ɛa = [ X+Y ] (10-6)Ɛb = -200(10-6)Ɛc = -180(10-6) x=100, y=100 (a) Prove that Ɛx = Ɛa and Ɛy = Ɛc. (b) Determine the shear strain, γxy and the normal strain, Ɛx and Ɛy.