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2 Pages

10_26

Course: MECHANICAL EM217, Spring 2011
School: Naval Academy
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Word Count: 445

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For 10.26 the beam and loading shown in Fig. P10.26, integrate the load distribution to determine (a) the equation of the elastic curve, (b) the deflection midway between the supports, (c) the slope at the left end of the beam, and (d) the support reactions Ay and By. Assume that EI is constant for the beam. Fig. P10.26 Solution Integrate the load distribution: d 4v x EI 4 = w0 sin dx L 3 x d v wL EI 3 = 0 cos +...

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For 10.26 the beam and loading shown in Fig. P10.26, integrate the load distribution to determine (a) the equation of the elastic curve, (b) the deflection midway between the supports, (c) the slope at the left end of the beam, and (d) the support reactions Ay and By. Assume that EI is constant for the beam. Fig. P10.26 Solution Integrate the load distribution: d 4v x EI 4 = w0 sin dx L 3 x d v wL EI 3 = 0 cos + C1 dx L x d 2v w L2 EI 2 = 0 2 sin + C1 x + C2 dx L x C1 x 2 dv w L3 EI = 0 3 cos + + C2 x + C3 dx L 2 w0 L4 x C1 x3 C2 x 2 EI v = 4 sin + + + C3 x + C4 L 6 2 Boundary conditions and evaluate constants: d 2v at x = 0, M = EI 2 = 0 dx d 2v w0 L2 ( L) at x = L, M = EI 2 = 0 sin + C1 ( L) = 0 2 dx L at x = 0, v = 0 at x = L, v = 0 w0 L4 4 sin ( L) L C2 = 0 C1 = 0 C4 = 0 + C3 ( L) = 0 C3 = 0 (a) Elastic curve equation: EI v = w0 L4 4 sin x w0 L4 x v = 4 sin EI L L Ans. (b) Deflection midway between the supports: vx = L / 2 = w0 L4 ( L / 2) w L4 sin = 40 4 EI L EI Ans. (c) Slope at the left end of the beam: EI dv dx = A EI = A w0 L3 3 cos (0) L = w0 L3 3 A = w0 L3 3 EI Ans. Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful. (d) Support reactions Ay and By: d 3v wL (0) w0 L VA = EI 3 = 0 cos = dx x = 0 L VB = EI d 3v dx 3 = x= L w0 L cos ( L) L = w0 L Ay = w0 L Ans. By = w0 L Ans. Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.
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Naval Academy - MECHANICAL - EM217
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Naval Academy - MECHANICAL - EM217
12.5 A tee-shaped flexural member (Fig. P12.5b) is subjected to an internal axial force of 2,200lb, an internal shear force of 1,600 lb, and an internal bending moment of 4,000 lb-ft, as shownin Fig. P12.5a. Determine the normal and shear stresses at po
Naval Academy - MECHANICAL - EM217
12.12 A 2.5-in.-diameter solid aluminum post issubjected to a horizontal force of V = 6 kips, avertical force of P = 15 kips, and a concentratedtorque of T = 22 kip-in., acting in the directionsshown in Fig. P12.12. Assume L = 4.5 in.Determine the no
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
14.10 The pressure tank in Fig. P14.10 is fabricatedfrom spirally wrapped metal plates that are welded atthe seams in the orientation shown. The tank has aninside diameter of 600 mm and a wall thickness of 5mm. Determine the largest allowable gage pre
Naval Academy - MECHANICAL - EM217
14.14 A strain gage is mounted to the outersurface of a thin-walled boiler as shown in Fig.P14.14. The boiler has an inside diameter of 60.0in. and a wall thickness of 1.000 in., and it ismade of stainless steel [E = 28,000 ksi; = 0.27].Determine:(a
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
14.17 A strain gage is mounted at an angle of 30 with respect to the longitudinal axis of the cylindricalpressure vessel shown in Fig. P14.17. The pressure vessel is fabricated from aluminum [E = 10,000 ksi; = 0.33], and it has an inside diameter of 48
Naval Academy - MECHANICAL - EM217
15.17 A hollow shaft is subjected to an axial load P and atorque T, acting in the directions shown in Fig. P15.17.The shaft is made of aluminum [E = 70 GPa; = 0.33],and it has an outside diameter of 100 mm and an insidediameter of 90 mm. A strain gage
Naval Academy - MECHANICAL - EM217
15.20 A flanged-shaped flexural member is subjected to an internal axial force of P = 8.5 kN, an internalshear force of V = 13.2 kN, and an internal bending moment of M = 2.1 kN-m, as shown Fig. P15.20a.Determine the principal stresses and the maximum s
Naval Academy - MECHANICAL - EM217
15.39 A short rectangular post supports compressive loads of P = 175 kN and Q = 90 kN as shown inFig. P15.39a. A top view of the post showing the locations where loads P and Q are applied to the top ofthe post is shown in Fig. P15.39b. Determine the ver
Naval Academy - MECHANICAL - EM217
15.45 A 1.25-in.-diameter solid shaft is subjected toan axial force of P = 360 lb, a vertical force of V =215 lb, and a concentrated torque of T = 430 lb-in.,acting in the directions shown in Fig. P15.45. AssumeL = 4.5 in. Determine the normal and she
Naval Academy - MECHANICAL - EM217
15.48 A steel pipe with an outside diameter of 95 mmand an inside diameter of 85 mm supports theloadings shown in Fig. P15.48.(a) Determine the normal and shear stresses on thetop surface of the pipe at point H.(b) Determine the principal stresses an
Georgia Tech - MATERIALS - 3720
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Naval Academy - MECHANICAL - EM217
16.4 A WT205 30 structural steel section (see Appendix B for cross-sectional properties) is used for a6.5-m column. Assume pinned connections at each end of the column. Determine:(a) the slenderness ratio.(b) the Euler buckling load. Use E = 200 GPa fo
Georgia Tech - MATERIALS - 3720
SCHOOL OF POLYMER, TEXTILE & FIBER ENGINEERING PTFE 3720, EXAM 1 KEY SP/10 Dr. Fred L. CookFebruary 25, 2010HONOR STATEMENT By my signature below, I certify that I have neither given nor received aid in completing this exam: _ Signature _ Printed Name N
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Naval Academy - MECHANICAL - EM217
16.5 Determine the maximum compressive load that a HSS6 4 1/4 structural steel column (seeAppendix B for cross-sectional properties) can support if it is 24 ft long and a factor of safety of 1.92 isspecified. Use E = 29,000 ksi for the steel.SolutionT
Georgia Tech - MATERIALS - 3720
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Naval Academy - MECHANICAL - EM217
16.39 A stainless steel pipe with an outside diameter of 100mm and a wall thickness of 8 mm is rigidly attached to fixedsupports at A and B. The length of the pipe is L = 8 m, itselastic modulus is E = 190 GPa, and its coefficient of thermalexpansion
Georgia Tech - MATERIALS - 3720
Naval Academy - MECHANICAL - EM217
Georgia Tech - MATERIALS - 3720
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
13.52 A metal alloy plate is subjected to tensile stresses of x = 8ksi and y = 5 ksi (Fig. P13.52). The strains measured in the plateare x = +950 and y = +335 . Determine Poissons ratio and the elastic modulus E for the material.Fig. P13.52SolutionR
Naval Academy - MECHANICAL - EM217
13.58 On the free surface of an aluminum [E = 70 GPa; = 0.35]component, the strain rosette shown in Fig. P13.58 was used to obtainthe following normal strain data: a = 980 b = 870 , and c =400 . Determine the normal stress that acts along an axis that
Naval Academy - MECHANICAL - EM217
The strain rosette shown in the figure was used to obtain normal straindata at a point on the free surface of a machine component.(a) Determine the strain components x, y, and xy at the point.(b) Determine the principal strains and the maximum in-plane
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM217
Naval Academy - MECHANICAL - EM319
Naval Academy - MECHANICAL - EM319
Naval Academy - MECHANICAL - EM319
Naval Academy - MECHANICAL - EM319
Naval Academy - MECHANICAL - EM319
Naval Academy - MECHANICAL - EM319
Naval Academy - MECHANICAL - EM319