3.3 A steel wire of length L = 20 cm is subjected to nonuniform heating such that the exten- sional strain is £x=k(x/L), where k=2 x 10² and x is the distance of a point from one end of the wire. Find the length of the deformed wire. Ans: 20.1 cm.
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- - 7.2-26 The strains on the surface of an experiment al device made of pure aluminum (E = 70 GPa. v = 0.33) and tested in a space shuttle were measured by means of strain gages. The gages were oriented as shown in the figure. and the measured strains were = 1100 X 106, h = 1496 X 10.6, and = 39.44 X l0_. What is the stress o in the x direction?Use the principle of Strain energy due to direct stresses strength of materials 24.7. Show that the direct strain-component in the y-direction is given by (Fig. 4.6). Figure 4.7 (Evv)s an ay Ay A x Ax Ay D' any Ay Figure 4.6 1 Ax
- The steel railroad increases its length when exposed to heat from 70°F to 95°F. The coefficient of thermal expansion is 11.7 x 10€ m/m-°C. Find the strain. A. 4.53 x 10-4 B. 2.625 x 104 C. 1.625 x 10-4 D. 3.53 x 10-4The state of strain in a plane element is Ex = -300 x 10-6 , Ey= 450 x 10-6, and Yxy = 275 x 10-6. (a) Use the strain transformation equations to determine the equivalent strain components on an element oriented at an angle of 0 = 30° counterclockwise from the original position. (b) Sketch the deformed element due to these strains within the x-y plane.A 20 m steel rod is heated from 26°C to 46°C. Find the total elongation of the rod if coefficient of the thermal expansion of steel is 11.5 x 10-6 m/m-°C. A. 4.60 mm B. 2.34 mm C. 6.78 mm D. 7.34 mm
- Determine the elastic tensile load "F" that acts on mild steel specimen of Diameter 5 mm & Modulus of Elasticity 207 GPa. It is found that the specimen has undergone an extension of 1.2 mm due to the elastic load "F". Also, determine the length "L" of the specimen, if the strain-induced due to the load "F" on the specimen is 3 x 10-³. Solution Cross-sectional Area, A (in mm²) = Tensile Stress, (in N/mm²) = Tensile Load, (in N) = Length of the Specimen (in mm)Question 4 A steel rod is subjected to a gradually applied load (F) which gave a rise to a maximum sress of 200 MPa. The rod is 250 mm long and one part of its length is square and the remainder is cireular with a diameter of 25 mm. If the total strain energy in the rod and modulus elasticity of the material is 1.3 J and 200 GPa, determine the following: 4.1 The applied bad F 4.2 The total extension of the bar 4.3 The length of the square portion of the bar The suddenly applied load that will induce the same amount of energy The load that falls from a height of 8 mm induces 1,3 J in the bar. 4.4 4.52. The stress-strain behavior of a ductile cast iron of diameter 15.8mm and a gauge length of 60.80mm is shown below, 400 300 200 100 0.00 0.10 Strain Determine the following: (a) the modulus of elasticity (b) yield strength at a strain offset of 0.002. Stress (MPa)
- 2-The strain of a component, which has a tensile modulus of 5 X 105 MPa, and subjected to a stress of 7000KPa, isDetermine the elastic tensile load "F" that acts on mild steel specimen of Diameter 9 mm & Modulus of Elasticity 201 GPa. It is found that the specimen has undergone an extension of 1 mm due to the elastic load "F". Also, determine the length "L" of the specimen, if the strain- induced due to the load "F" on the specimen is 3.6 x 10-³. Solution Cross-sectional Area, A (in mm²) = 63.617 One possible correct answer is: 63.617251235193 Tensile Stress, (in N/mm²) 723.6 One possible correct answer is: 723.6 Tensile Load, (in N) = = 46033.261 One possible correct answer is: 46033.442993786 Length of the Specimen (in mm) 4.366 X One possible correct answer is: 277.77777777778Two round rods, one of steel, the other of brass, are joined end to end. Each rod is 0.5 m long and 2 cm in diameter. The combination is subjected to a tensile force of 5000 N. Find the strain in each rod. Young's Modulus of Steel use 20×10¹⁰ Pa, of brass use 10×10¹⁰ Pa. Find the elongation of each rod.