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The 45° strain rosette is mounted on the surface of a shell. The following readings are obtained for each gage:
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Chapter 14 Solutions
EBK STATICS AND MECHANICS OF MATERIALS
- 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 Xarrow_forwardQ4 A three strain gages have been attached directly to a piston used to raise a medical chair, the strain gages give strains as ɛa = 80 µ , Ep = 60 µ and Ec = 20 µ . Determine the principal strains and the principal strain directions for the given set of strains. And Compute the strain in a direction -30° (clockwise) with the x axis. a,x A c.y Pumparrow_forwardThe strain components Ex, Ey, and Yxy are given for a point in a body subjected to plane strain. Using Mohr's circle, determine the principal strains, the maximum in-plane shear strain, and the absolute maximum shear strain at the point. Show the angle 0p, the principal strain deformations, and the maximum in-plane shear strain distortion in a sketch. Ex = 0 μE, Ey = 310 με, Yxy = 280 μrad. Enter the angle such that -45° ≤ 0,≤ +45° Answer: Ep1 = Ep2 = Ymax in-plane = Yabsolute max. = 0p = με με urad uradarrow_forward
- The 45° strain rosette is mounted on the surface of a pressure vessel. The following readings are obtained for each gage: Pa = 475(10-6), Pb = 250(10-6), and Pc = -360(10-6). Determine the in-plane principal strainsarrow_forwardFor the state of a plane strain with εx, εy and γxy components: (a) construct Mohr’s circle and (b) determine the equivalent in-plane strains for an element oriented at an angle of 30° clockwise. εx = 255 × 10-6 εy = -320 × 10-6 γxy = -165 × 10-6arrow_forwardQ4 A three strain gages have been attached directly to a piston used to raise a medical chair, the strain gages give strains as Ea = 80 µ , Eb = 60 µ and Ec = 20 u . Determine the principal strains and the principal strain directions for the given set of strains. And Compute the strain in a direction -30° (clockwise) with the x axis. 45 Pumparrow_forward
- The strain components ɛ, Ey, and yxy are given for a point in a body subjected to plane strain. Using Mohr's circle, determine the principal strains, the maximum in-plane shear strain, and the absolute maximum shear strain at the point. Show the angle 0p, the principal strain deformations, and the maximum in-plane shear strain distortion in a sketch. Ex = 0 µE, ɛ, = 320 µɛ, Vxy = 240 µrad. Enter the angle suen that -45° s 0,s+45°.arrow_forwardI 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 étvarrow_forwardA material is subjected to the following strain system,ex=200x10-6, ey=-56x10-6,yxy=230x10-6. Using graphical method, determine A. The principal strains B. The directions of principal strain axes C. The linear strain on an axis inclined at 50o counter clockwise to the direction of ex Given that young's modulus for the material is 207GN/m2 and the poisson's ratio is 0.27, determine the principal stressesarrow_forward
- The 60° strain rosette is mounted on the surface of the bracket. The following readings are obtained for each gage: Pa = -780(10-6), Pb = 400(10-6), and Pc = 500(10-6). Determine (a) the principal strains and (b) the maximumin-plane shear strain and associated average normal strain. In each case show the deformed element due to these strains.arrow_forwardThe strain components ɛ, Ey, and yy are given for a point in a body subjected to plane strain. Using Mohr's circle, determine the principal strains, the maximum in-plane shear strain, and the absolute maximum shear strain at the point. Show the angle 0, the principal strain deformations, and the maximum in-plane shear strain distortion in a sketch. Ex = 300 µe, ɛ, = -710 pe, Vxy = -440 urad. Enter the angle such that -45°s0,s +45°. Answer: Ep1= pe Ep2= με Ymax in-plane = prad Yabsolute max. prad Əp =arrow_forwardThe strain components for a point in a body subjected to plane strain are ɛx = 630 µɛ, ɛy = 940µe and yxy = 1193 urad. Using Mohr's circle, determine the principal strains (ɛp1 > Ep2), the maximum inplane shear strain yip, and the absolute maximum shear strain ymax at the point. Show the angle 0, (counterclockwise is positive, clockwise is negative), the principal strain deformations, and the maximum in-plane shear strain distortion in a sketch. Answers: Ep1 με. %3D Ep2 = HE. Vip = prad. Vmax prad. Op =arrow_forward
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