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ME3180_HW1_Solutions_Spring2012

# ME3180_HW1_Solutions_Spring2012 - Georgia Institute of...

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Unformatted text preview: Georgia Institute of Technology ME 3180: Machine Design Spring 2012: Sections A, RCC, RPK, and RPY Homework #1 Assigned on Jan. 11, 2012 Due in class on Jan. 19, 2012 Problem 1 For the simply-supported beam shown in the ﬁgure, calculate the reactions at the supports and plot the shear-force and bending-moment diagrams. Label the diagrams properly and provide values at all key points. 9kN 5kN Problem 2 A part experiences a static loading condition that results in the following plane stress state: 6x = 15 kpsi 03, = -8 kpsi Txy = ‘8 a) What are the principal stresses? b) What is the orientation of the principal axes relative to the given axes? c) What is the maximum shear stress? Problem 3 If the maximum shear stress of a round steel bar cannot exceed 140 MPa while transmitting a steady torque of 340 Nm, what is the required diameter of the bar? Brow A diagonal aluminum alloy tension rod (0.5 inch diameter, 8 foot length) is used in a rectangular frame to prevent collapse. If the maximum allowable tensile stress is 20 kpsi, determine how much the rod must be stretched to develop this stress. Problem 5 Three round, 1.25 inch diameter bars are made of SAE1030 HR (hot-rolled) steel but are different lengths of 5 inches, 30 inches, and 60 inches, respectively. Compare the load- supporting capability of the three bars if they are loaded in compression and the ends are assumed to be: a) Rounded-rounded. b) Fixed-ﬁxed. c) Free-ﬁxed. d) Rounded-ﬁxed. 0 500 1000 1500 x (mm) 2500 .. .. . . . . ‘ . V . . . E 1000 M1: zqw-Mmmoo» \ 4 w» > Mo; ». [We (Um _I O 500 1000 1500 x (mm) 500 EM/‘éf hp 9:- > 2r“;ch :> P“: Aﬂq‘lgfc 2 Lee vow a: s» l» a, “ﬁg: 3 row/m! laws 0C ﬂlé I030 #51 Wed (75: 1.75 Snakes SAE 1030 ML 9726/ S = 2(00 MPa (37.; szD (woe A—zo) E Ti 3000'”) F9; (Tame 4,5) ,0: Simﬂxes) '50 had“, \$0 Maﬁa; a3VMnJeJ~WeJ¢ C3! {or I or 1) game's Fiﬁd~€5¢ej :2) C: L} (or I ash/.1) (See WW) C3 Free- 9m} é C: 1‘; Cari W i) +2 A) mew-9M a c=2 can v- m E: Syt=Syc= 3.00307 psI 3.75304 psi Using theoretical values for the end conditions (see Table 4—2 In Shigiey 9th edition) Diameter In. Area In."2) I In.'\4) k In. len h In. C Sr)d or I/k 1) Pcr lbs. 3) Rounded-rounded 1.25 1.227 0.1198 0.3125 5 1 125.7 4.56E+04 1.25 1.227 0.1198 0.3125 30 1 125.7 3.26E+04 1.25 1.227 0.1198 0.3125 60 1 125.7 9.86E+03 b) Fixed—ﬁxed 1.25 1.227 0.1198 0.3125 5 4 251.3 4.59E+04 1.25 1.227 0.1198 0.3125 30 4 251.3 4.27E+04 1.25 1.227 0.1198 0.3125 60 4 251.3 3.26E+04 c) Free-ﬁxed 1.25 1.227 0.1198 0.3125 5 0.25 62.8 4.45E+04 1.25 1.227 0.1198 0.3125 30 0.25 62.8 9.86E+03 1.25 1.227 0.1198 0.3125 60 0.25 62.8 2.46E+03 d) Rounded-ﬁxed 1.25 1.227 0.1198 0.3125 5 2 177.7 4.58E+04 1.25 1.227 0.1198 0.3125 30 2 177.7 3.93E+04 1.25 1.227 0.1198 0.3125 60 2 177.7 1.97E+04 Using conservative values for end conditions (see Table 4-2 in Shlgiey 9th edition) Diameter in. Area in."2 I ln."4 k In. Ien h In. C 5r 0 or Ilk 1) Per lbs.) 3) Rounded-rounded 1.25 1.227 0.1198 0.3125 5 1 125.7 4.56E+04 1.25 1.227 - 0.1198 0.3125 30 1 125.7 3.26E+04 1.25 1.227 0.1198 0.3125 60 1 125.7 9.86E+03 b) Fixed-ﬁxed 1.25 1.227 0.1198 0.3125 5 1 125.7 4.56E+04 1.25 1.227 0.1198 0.3125 30 1 125.7 3.26E+04 1.25 1.227 0.1198 0.3125 60 1 125.7 9.86E+03 c) Free-ﬁxed 1.25 1.227 0.1198 0.3125 5 0.25 62.8 4.45E+04 1.25 1.227 0.1198 0.3125 30 0.25 62.8 9.86E+03 1.25 1.227 0.1198 0.3125 60 0.25 62.8 2.46E+03 d) Rounded-ﬁxed 1.25 1.227 0.1198 0.3125 5 1 125.7 4.56E+04 1.25 1.227 0.1198 0.3125 30 1 125.7 3.26E+04 1.25 1.227 0.1198 0.3125 50 1 125.7 9.86E+03 Using recommended values for end conditions (see Table 4-2 In Shlgley 9th edition) Diameter (ln.) Area (In.'\2) I (In.’\4) k (in.) length In. C (Sr)d or l/k 1 Pcr (lbs.) 3) Rounded-rounded 1.25 1.227 0.1198 0.3125 5 1 125.7 4.56E+04 1.25 1.227 0.1198 0.3125 30 1 125.7 3.26E+04 1.25 1.227 0.1198 0.3125 60 1 125.7 9.86E+03 b) Fixed-ﬁxed 1.25 1.227 0.1198 0.3125 5 1.2 137.7 4.57E+04 1.25 1.227 0.1198 0.3125 30 1.2 137.7 3.48E+O4 1.25 1.227 0.1198 0.3125 60 1.2 137.7 1.18E+04 c) Free-fixed 1.25 1.227 0.1198 0.3125 5 0.25 62.8 4.45E+04 1.25 1.227 0.1198 0.3125 30 0.25 62.8 9.86E+03 1.25 1.227 0.1198 0.3125 60 0.25 62.8 2.46E+03 d) Rounded—fixed 1.25 1.227 0.1198 0.3125 5 1.2 137.7 4.57E+04 1.25 1.227 0.1198 0.3125 30 1.2 137.7 3.48E+O4 1.25 1.227 0.1198 0.3125 60 1.2 137.7 1.18E+04 ...
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