Materials Science And Engineering Properties
1st Edition
ISBN: 9781111988609
Author: Charles Gilmore
Publisher: Cengage Learning
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Chapter 12, Problem 5ETSQ
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Find effective elasticity (stiffness) tensor of a two-phase layered composite material
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A composite beam is made of two brass [E = 99 GPa] plates bonded to an aluminum [E = 63 GPa] bar, as shown. The beam is subjected to a bending moment of 2210 N-m acting about the z axis. Assume b=44 mm, d1=28 mm, d2=13 mm. Determine:(a) the maximum bending stresses σbr, σal in the brass plates and the aluminum bar.(b) the stress in the brass σbrjσbrj at the joints where the two materials are bonded together.
A composite column is formed by placing a steel bar, 20 mm in diameter and 200 mm long, inside an alloy cylinder of the same length whose internal and external diameters are 20 mm and 25 mm, respectively. The column is then subjected to an axial load of 50 kN. If E for steel is 200 OOO N/mm’ and E for the alloy is 70 000 N/mm’, calculate the stress in the cylinder and in the bar, the shortening of the column and the strain energy stored in the column.
Chapter 12 Solutions
Materials Science And Engineering Properties
Ch. 12 - Prob. 1CQCh. 12 - Prob. 2CQCh. 12 - Prob. 3CQCh. 12 - Prob. 4CQCh. 12 - Prob. 5CQCh. 12 - Prob. 6CQCh. 12 - Prob. 7CQCh. 12 - Prob. 8CQCh. 12 - Composite _________ is produced by laying fibers...Ch. 12 - Prob. 10CQ
Ch. 12 - Prob. 11CQCh. 12 - Prob. 12CQCh. 12 - Prob. 13CQCh. 12 - Prob. 14CQCh. 12 - Prob. 15CQCh. 12 - Prob. 16CQCh. 12 - Prob. 17CQCh. 12 - Prob. 18CQCh. 12 - Prob. 19CQCh. 12 - Prob. 20CQCh. 12 - Prob. 21CQCh. 12 - Prob. 22CQCh. 12 - Prob. 23CQCh. 12 - Prob. 24CQCh. 12 - Prob. 25CQCh. 12 - Prob. 26CQCh. 12 - Prob. 27CQCh. 12 - Prob. 28CQCh. 12 - Prob. 1ETSQCh. 12 - Prob. 2ETSQCh. 12 - Prob. 3ETSQCh. 12 - Prob. 4ETSQCh. 12 - Prob. 5ETSQCh. 12 - Prob. 6ETSQCh. 12 - Prob. 7ETSQCh. 12 - Prob. 8ETSQCh. 12 - Prob. 9ETSQCh. 12 - Prob. 10ETSQCh. 12 - In Example Problem 12.1, a uniaxial composite...Ch. 12 - Prob. 12.2PCh. 12 - Prob. 12.3PCh. 12 - Prob. 12.4PCh. 12 - Prob. 12.5PCh. 12 - Prob. 12.6PCh. 12 - Estimate the transverse tensile strength of the...Ch. 12 - Prob. 12.8PCh. 12 - Prob. 12.9PCh. 12 - Prob. 12.10PCh. 12 - Prob. 12.11PCh. 12 - Prob. 12.12PCh. 12 - Prob. 12.13PCh. 12 - Prob. 12.14PCh. 12 - Prob. 12.15PCh. 12 - Prob. 12.16PCh. 12 - Prob. 12.17P
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- A ceramic matrix composite contains internal flaws as large as 0.001 cm in length. The plane strain fracture toughness of the composite is 45 MPaÖm, and the tensile strength is 550 Mpa. Will the stress cause the composite to fail before the tensile strength is 550 MPa. Will the stress cause the composite to fail before the tensile strength is reached? Assume that f=1.arrow_forwardA composite beam is made of two brass [E = 96 GPa] plates bonded to an aluminum [E = 62 GPa] bar, as shown. The beam is subjected to a bending moment of 2260 N-m acting about the z axis. Assume b=53 mm, d1=48 mm, d2=14 mm. Determine:(a) the maximum bending stresses σbrσbr, σalσal in the brass plates and the aluminum bar.(b) the stress in the brass σbrjσbrj at the joints where the two materials are bonded together.arrow_forwardWrite the three functions of the matrix phase in fiber-reinforced composites (FRPs). Briefly state the reason for the need for a strong bond between the fibers and the matrix.arrow_forward
- The stress-strain diagram of reinforcement steel having a cross-sectional diameter of 12 mm diameter and 100 mm gage length is determined after its tensile strength test as follows. Based on the stress-strain diagram determine the followings properties of the material (Poisson’s ratio of the material is 0.32) a) Resilienceb) Shear modulusc) Bulk modulusd) Ductility as described by the percent change in lengtharrow_forwardA brass specimen of the circular cross-section is fractured at 151 kN force and the final length of the specimen at fracture is 49 mm. The fracture strength of the specimen is found to be 74 kN/mm2. The percentage of elongation of the specimen is 42 %. Determine the following (i) Diameter of the specimen ii) Initial length of the specimen iii) Stress under an elastic load of 16 kN iv) Young's Modulus if the elongation is 1.6 mm at 16 kN (v) Final diameter if the percentage of reduction in area is 20 % solve: Initial Cross-sectional Area (in mm2) = The Diameter of the Specimen (in mm) = Initial Length of the Specimen (in mm) =arrow_forwardThe composite bar shown is rigidly attached to the two supports. The left portion of the bar is copper, of uniform cross-sectional area 80 c?^2 and length 30 cm. The right portion is aluminum, of uniform cross-sectional area 20 c?2 and length 20 cm. At a temperature of 26℃ the entire assembly is stress free. The temperature of the structure drops and during this process the right support yields 0.025 mm in the direction of the contracting metal. Determine the minimum temperature to which the assembly may be subjected in order that the stress in the aluminum does not exceed 160 MPa. For copper E = 200 GPa, ? = 17x10^-6/℃, and for Aluminum E = 80 GPa, ? = 23x10^-6/℃.arrow_forward
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