The minimum strain at failure in tension steel having yield stress modulus E = 200 GPa, as per Limit State Method of Design, is = 415 MPa and Young's
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- An aluminum alloy [E = 74 GPa; v = 0.33; a = 23.0 x 10-6/°C] plate is subjected to a tensile load P. The plate has a depth of d = 265 mm, a cross-sectional area of A = 5300 mm², and a length of L= 4.2 m. The initial longitudinal normal strain in the plate is zero. After load P is applied and the temperature of the plate has been increased by AT = 57°C, the longitudinal normal strain in the plate is found to be 2920 με. Determine: (a) the magnitude of load P. (b) the change in plate depth Ad. L P Answer: (a) P = i (b) Δd = i kN mmAn aluminum alloy [E = 73 GPa; v = 0.33; a= 23.0 x 10-6/°C] plate is subjected to a tensile load P. The plate has a depth of d = 250 mm, a cross-sectional area of A = 6900 mm², and a length of L = 5.9 m. The initial longitudinal normal strain in the plate is zero. After load P is applied and the temperature of the plate has been increased by AT = 50°C, the longitudinal normal strain in the plate is found to be 2400 με. Determine: (a) the magnitude of load P. (b) the change in plate depth Ad. L Answer: (a) P = i (b) Δd = KN mm1.4-7 The data shown in the table below were obtained from a tensile test of high-strength steel. The test specimen had a diameter of 13 mm and a gage length of 50 mm (see figure for Prob. 1.4-3). At fracture, the elongation between the gage marks was 3.0 mm and the minimum diameter was 10.7 mm. Plot the conventional stress-strain curve for the steefor the steel and determine the proportional limit, modulus of elastics of elastic- ity (i.e., the slope of the initial part of the stress-strain,tress-strain curve), yield stress at 0.1% offset, ultimate stress, percent, elongation in 50 mm, and percent reduction in area. 'ess, percent area. TENSILE-TEST DATA FOR PROB. 1.4-7 Elongation (mm) 0.005 0.015 0.048 Load (kN) 5 10 30 50 0.084 60 0.099 64.5 0.109 67.0 0.119 68.0 0.137 69.0 0.160 70.0 0.229 72.0 0.259 76.0 0.330 84.0 0.584 92.0 0.853 100.0 1.288 112.0 2.814 113.0 Fracture
- An aluminum alloy [E = 67 GPa; ν = 0.33; α = 23.0 × 10–6/°C] plate is subjected to a tensile load P. The plate has a depth of d = 225 mm, a cross-sectional area of A = 5100 mm2, and a length of L = 4.1 m. The initial longitudinal normal strain in the plate is zero. After load P is applied and the temperature of the plate has been increased by ΔT = 63°C, the longitudinal normal strain in the plate is found to be 2900 με. Determine: (a) the magnitude of load P. (b) the change in plate depth Δd.A steel component is subjected to alternate cyclical loading. The steel follows Basquin's law for high cycle fatigue, o, x N = C, (where the stress amplitude is in MPa). Ignore the geometric detail and assume that Marin's modifying factors are all equal to 1. You are given the minimum stress ain = -213 MPa, the maximum stress omax = 213 MPa. The material data are Tensile strength oUTS = 539 MPa, Basquin's constant c, = 875 MPa, Basquin's exponent a = 0.085. a) Calculate the stress ratio R, the stress amplitude o, in MPa and the mean stress am in MPa. The answers are acceptable with a tolerance of 0.01 for R and of 1 MPa the stresses. R: MPa MPа b) Calculate the corresponding life, in 10° cycles, (tolerance of 0.1 106 cycles) N :A steel 0.6 inch×1.2 inch steel 90 m long is subjected to a 45 KN tensile load along its lenght.If poison's ratio is 0.3 Find: A. The deformation along its lenght. B. The deformation along its thickness. C. The defirmation along uts width. D. The lateral strain.
- A steel with E = 29 000 ksi with a rectangular cross-section is bent over a rigid mandrel with R = 15 in as shown in the figure. If the maximum flexural stress in the bar is not to exceed the yield strength of 36 ksi, determine the allowable thickness h of the bar.A state of plane stress (σ3=0) occurs at a critical point of a mild steel machine component (see Figure 1 below). As a result of several tension tests, it has been found that the tensile yield strength is = 250MPa for the grade of steel used. (a) Determine the factor of safety (FS) with respect to yield using (i) the maximum shear stress criterion and (ii) the maximum distortion energy (von Mises) criterion. (b) Graph the Tresca Hexagon and the von Mises oval for this material and note the location of the given state of plane stress as a point on the graph.As shown, an aluminium alloy construction BCD with a circular cross section is fixed at end B and affected by a force of 150 N at the free end D. The diameter of the cross-section a-a is 20 mm. The yield strength of the material is 80 MPa: a) Determine the stresses at point A of the a-a cross-section. As indicated in the picture, draw the stress element in Cartesian coordinates and specify the stress values.(b) Calculate the factor of safety, n for Tresca, and the von Mises yield criterion to see if the structure would yield based on the stresses at point A.(c) In the major stress area, draw the yield loci of both criteria and indicate the operational stress state & why is the Rankine failure criterion inappropriate for aluminium alloys?
- An aluminum alloy [E = 70 GPa; v = 0.33; a = 23.0×10-6/°C] bar is subjected to a tensile load P. The bar has a depth of d = 260 mm, a cross-sectional area of A = 14720 mm2, and a length of L = 5.5 m. The initial longitudinal normal strain in the bar is zero. After load P is applied and the temperature of the bar has been increased by AT = 46°C, the longitudinal normal strain is found to be 1680 µɛ. % D Calculate the change in bar depth d after the load P has been applied and the temperature has been increased. L P Answer: Ad = i mmA strip of high-strength steel has a length of 30 cm and a cross section of 1 mm by 20 mm. The modulus of elasticity is 200 GPa and Poison’s ratio is 0.27. It is subjected to an axial load of 15000 N, and it is instrumented with two axial strain gauges with R= 120 Ω and a gauge factor of 2.10. The two fixed resistors are also 120 Ω, and the supply voltage is 2.5 V. The bridge is adjusted to zero voltage output before load is applied. Find the output of the bridge with load applied.Problem 1.5-2 A bar of length 2.0 m is made of a structural stoel having the stres-strain dingram shown in the figure. The yield stresa of the steel is 250 MPa and the slope of the initial lincar part of the stress-strain curve (modulus of elasticity) is 200 GP. The bar is loaded axially until it eklongates 6.5 mm, and then the load is removod. How does the final length of the bar compare with its orig- inal length? Hint: Ue the concepts illustrated in Fig. 1-36h) MP 300 200 100 0.002 0.004 0.006