HW_CH5

HW_CH5 - ' 1323 = ' 1 2 1 3 - 3 2 + = Stress Element for...

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Unformatted text preview: ' 1323 = ' 1 2 1 3 - 3 2 + = Stress Element for Problem 5-1a 3. Using equatoion 5.7c, the von Mises stress is FIGURE 5-1aA 3 207- = 2 = 1 1207 = 2. From Problem 4-1 a , the principal stresses are 1. Draw the stress element, indicating the x and y axes. Solution: See Figure 5-1a and Mathcad file P0501a. zx = yz = xy 500 = z = y = x 1000 = Given: Statement: A differential stress element has a set of applied stresses on it as indicated in row a of Table P5-1. For row a , draw the stress element showing the applied stresses. Find the principal stresses and the von Mises stress. PROBLEM 5-1a Coulomb-Mohr N ACM S ut S uc S uc 1A S ut 3A - = N ACM 13.4 = Modified-Mohr N AMM S ut 1A = N AMM 16.3 = 4. From Problem 4-33a, the principal stresses at Point B are 1B 16.13 MPa = 2B MPa = 3B 16.13- MPa = 5. Using the two nonzero stresses, the slope of the load line on a 1- 3 graph is m 3B 1B = m 1- = This intersects the failure boundaries in the fourth quadrant. For the Coulomb-Mohr diagram (see Figure 5-9 in the text) there is a single, straight line in this quadrant. For the modified-Mohr theory, the load line will intersect the boundary at the point ( S ut , - S ut ) Figure 5-11 in the text. 6. Determine the factor of safety at point B Coulomb-Mohr N BCM S ut S uc S uc 1B S ut 3B - = N BCM 16.1 = PROBLEM 5-35a Statement: Calculate the safety factor for the bracket in Problem 5-33 using the Coulomb-Mohr and th modified Mohr effective stress theories. Comment on their appropriateness. Assume a brittle material strengt as given below. Units: MPa 10 6 Pa = Given: Tensile strength S ut 350 MPa = Compressive strength S uc 1000 MPa = Solution: See Mathcad file P0535a. 1. From Problem 4-33a the principal stresses at point A are 1A 21.46 MPa = 2A MPa = 3A 13.08- MPa = 2. Using the two nonzero stresses, the slope of the load line on a 1- 3 graph is m 3A 1A = m 0.61- = This intersects the failure boundaries in the fourth quadrant. For the Coulomb-Mohr diagram (see Figure 5-9 in the text) there is a single, straight line in this quadrant. For the modified-Mohr theory, the load line will intersect the boundary at a point similar to B' in Figure 5-11 in the text. 3. Determine the factor of safety at point A N 21.7 = N S ut 1B = 1 is maximum so C 3 16.1 MPa = C 3 1 2 3B 1B- S uc- 2 S ut + S uc- 3B 1B + ( 29 + = C 2 5.6 MPa = C 2 1 2 2B 3B- S uc- 2 S ut + S uc- 2B 3B + ( 29 + = C 1 10.5 MPa = C 1 1 2 1B 2B- S uc- 2 S ut + S uc- 1B 2B + ( 29 + = Point B N 16.3 = N S ut 1A = 1 is maximum so C 3 18.5 MPa = C 3 1 2 3A 1A- S uc- 2 S ut + S uc- 3A 1A + ( 29 + = C 2 4.6 MPa = C 2 1 2 2A 3A- S uc- 2 S ut + S uc-...
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This note was uploaded on 07/23/2011 for the course EML 4501 taught by Professor Staff during the Spring '11 term at UNF.

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HW_CH5 - ' 1323 = ' 1 2 1 3 - 3 2 + = Stress Element for...

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