A circle of a diameter d = 200 mm is etched on a brass plate (see figure). The plate has dimensions of 400 x 400 x 16 mm. Forces are applied to the plate, producing uniformly distributed normal stresses a, = 53 MPa and o, = -14 MPa. Calculate the following quantities. (Assume that the material is linearly elastic with modulus of elasticity E = 100 GPa and Poisson's ratiov = 0.34.)

Structural Analysis
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Chapter2: Loads On Structures
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A circle of a diameter d = 200 mm is etched on a brass plate (see figure).
The plate has dimensions of 400 x 400 x 16 mm. Forces are applied to the plate, producing uniformly distributed normal stresses o. = 53 MPa and o = -14 MPa. Calculate the following quantities. (Assume that the material is linearly elastic with modulus of elasticity
E = 100 GPa and Poisson's ratio v = 0.34.)
(a) the change in length Aac of diameter ac (in mm)
mm
(b) the change in length Abd of diameter bd (in mm)
mm
(c) the change At in the thickness of the plate (in mm)
mm
(d) the change AV in the volume of the plate (in mm3)
|mm3
(e) the strain energy U stored in the plate (in J)
(f) the maximum permissible thickness of the plate (in mm) when strain energy U must be at least 52.1 J
mm
(g) the maximum permissible value of normal stress o, when the change in volume of the plate cannot exceed 0.014% of the original volume (Enter the magnitude in MPa.)
MPa
Transcribed Image Text:A circle of a diameter d = 200 mm is etched on a brass plate (see figure). The plate has dimensions of 400 x 400 x 16 mm. Forces are applied to the plate, producing uniformly distributed normal stresses o. = 53 MPa and o = -14 MPa. Calculate the following quantities. (Assume that the material is linearly elastic with modulus of elasticity E = 100 GPa and Poisson's ratio v = 0.34.) (a) the change in length Aac of diameter ac (in mm) mm (b) the change in length Abd of diameter bd (in mm) mm (c) the change At in the thickness of the plate (in mm) mm (d) the change AV in the volume of the plate (in mm3) |mm3 (e) the strain energy U stored in the plate (in J) (f) the maximum permissible thickness of the plate (in mm) when strain energy U must be at least 52.1 J mm (g) the maximum permissible value of normal stress o, when the change in volume of the plate cannot exceed 0.014% of the original volume (Enter the magnitude in MPa.) MPa
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