Both portions of the rod ABC are made of an aluminum for which E = 70 GPa.Based on the given information find:1- deformation at A2- stress in BC3- Total strain4- If v (Poisson ratio is 0.25, find thelateral deformation of ABLast 3 student ID+ 300 mm=L2724AP=Last 2 student ID+ 300 KN2424Diameter Last 2 student ID+ 15 mmLast 3 student ID+ 500 mm=L1724CB24Q=Last 2 student ID+ 100 KN24Diameter Last 2 student ID+ 40 mm

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Answered: Both portions of the rod ABC are made…

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter7: Analysis Of Stress And Strain

Section: Chapter Questions

Problem 7.4.8P: - A specimen used in a coupon test has norm al stress ??. = 15 MPa (see figure). Using Mohr’s...

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- A specimen used in a coupon test has norm al stress ??. = 15 MPa (see figure). Using Mohr’s circle, find the state of stress on the element oriented at angle ? = 20° and show the full stress state on a sketch of a properly oriented element.
Solve the preceding problem if the thickness of the steel plate is. t = 12 mm. the gage readings are x = 530 × 10-6 (elongation) and y = -210 -× l0-6 (shortening), the modulus is E = 200 GPa, and Poisson’s ratio is v = 0.30.
Solve the preceding problem if the cross- sectional dimensions are b = 1.5 in. and h = 5.0 in., the gage angle is ß = 750, the measured strains are = 209 × 10-6 and B = -110 × 10, and the material is a magnesium alloy with modulus E = 6.0 X 106 psi and Poisson’s ratio v = 0.35.
Solve the preceding problem if the plate is made of aluminum with E = 72 GPa and Poisson’s ratio v = 0.33. The plate is loaded in biaxial stress with normal stress sx= 79 MPa, angle Ø = 18°, and the strain measured by the gage is e = 925 × 10-6.
A simply supported beam is subjected to point load P at mid-span. The normal stress on an element at mid-span is known to be ??x= 1.5 ksi. Determine the element stresses lilt is rotated through angle ? = 450• Show these stresses on a sketch of an element oriented at that angle.
An clement of material subjected to plane strain (see figure) has strains of x=280106 , y=420106 , and xy=150106 . Calculate the strains for an element oriented at an angle = 35°. Show these strains on a sketch of a properly oriented element.
The strength-to-weight ratio of a structural material is defined as its load-carrying capacity divided by its weight. For materials in tension, use a characteristic tensile stress obtained from a stress-strain curve as a measure of strength. For instance, either the yield stress or the ultimate stress could be used, depending upon the particular application. Thus, the strength-to-weight ratio RS/Wfor a material in tension is defined as Rs/w= in which a is the characteristic stress and 7 is the weight density. Note that the ratio has units of length. Using the ultimate stress Uas the strength parameter, calculate the strength-to-weight ratio (in units of meters) for each of the following materials: aluminum alloy 606I-T6, Douglas fir (in bending}, nylon. structural steel ASTM-A57.2, and a titanium alloy. Obtain the material properties from Tables [-1 and 1-3 of Appendix I. When a range of values is given in a table, use the average value.
The stresses on an element are sx= 1000 Psi. sy= 500 psi, and txy= 350 psi. Find the stresses acting on an element oriented at an angle 0 = 250. Show these stresses on the rotated element.
Solve the preceding problem if the diameter is 480 mm, the pressure is 20 MPa, the yield stress in tension is 975 MPa, the yield stress in shear is 460 MPa, the factor of safety is 2,75, the modulus of elasticity is 210 GPa, Poissorfs ratio is 0.28, and the normal strain must not exceed 1190 x 10" . For part (b), assume that the tank thickness is 8 mm and the measured normal strain is 990 x 10~ .
A brass plate with a modulus of elastici ty E = 16 X 106 psi and Poisson’s ratio a = 0.34 is loaded in biaxial stress by normal stresses r and cry. (sec figure). A strain gage is bonded to the plate at an angle 4 = 350 If the stress o is 10,700 psi and the strain means used by the gageise = 390 X 106.whatisthcmax- imum in-plane shear stress (Tr, ),. and shear strain (>‘ ).? What is the maximum shear strain (y ) in the x-: plane? What is the maximum shear strain (y ).. in the y-r plane?
Three round, copper alloy bars having the same length L but different shapes are shown, in the figure. The first bar has a diameter d over its entire length, the second has a diameter d over one-fifth of its length, and the third has a diameter d over one-fifteenth of its length. Elsewhere, the second and third bars have a diameter Id. All three bars are subjected to the same axial load P. Use the following numerical data: P = 1400 kN, L = 5m,d= 80 mm, E= 110 GPa. and v = 0.33. (a) Find the change in length of each bar. (b) Find the change in volume of each bar.
A circular cylindrical steel tank (see figure) contains a volatile fuel under pressure, A strain gage at point A records the longitudinal strain in the tank and transmits this information to a control room. The ultimate shear stress in the wall of the tank is 98 MPa, and a factor of safety of 2,8 is required. (a) At what value of the strain should the operators take action to reduce the pressure in the tank? (Data for the steel are modulus of elasticity E = 210 GPa and Poisson's ratio v = 0.30.) (b) What is the associated strain in the radial direction

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