Shear and Bending Moment Analysis for Beam Problems

School

University of California, Irvine**We aren't endorsed by this school

Course

ENGRMAE 52

Subject

Mechanical Engineering

Date

Dec 12, 2024

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Uploaded by ProfElectronLlama49

Problems 7.29 through 7.32 For the beam and loading shown, (a) draw the shear and bending-moment diagrams, (b) determine the maximum absolute value of the bending moment. o P Lk s = |<_u_.‘ T Fig. P7.31 Fig. P7.32 7.33 and 7.34 For the beam and loading shown, (a) draw the shear and bending-moment diagrams, (b) determine the maximum absolute val- ues of the shear and bending moment. Fig. P7.30 Fig. P7.33 Fig. P7.34 7.35 and 7.36 For the beam and loading shown, (a) draw the shear and bending-moment diagrams, (b) determine the maximum absolute val- ues of the shear and bending moment. 15 kN 25kN 20 kN 40KN 32KN L c - A L |D 1 m—f 7 N 08m ljm——l L-—D.Zm 03m’ 30kN “04m 06m 09m Fig. P7.35 Fig. P7.36 7.37 and 7.38 For the beam and loading shown, (a) draw the shear and bending-moment diagrams, (b) determine the maximum absolute val- ues of the shear and bending moment. 6 kibs 112 bips 45kips 1201 300 1b 120 Ib o RS ——— | LWJ——I——‘I-—» o . 20in. '15in. 2ft 2ft 2ft Fig. P7.37 Fig. P7.38

7.39 through 7.42 For the beam and loading shown, (a) draw the shear and bending-moment diagrams, (b) determine the maximum absolute values of the shear and bending moment. CORN 25 kim AT " 3 F 2m—] . sm 2m 30 kN/m A [ \kZmJ—L Im A 21t 8 kip: Fig. P7.39 Fig. P7.40 Fig. P7.41 7.43 Assuming the upward reaction of the ground on beam AB to be uni- formly distributed and knowing that P = wa, (a) draw the shear and bending-moment diagrams, (b) determine the maximum absolute val- ues of the shear and bending moment. lododad o] Fig. P7.43 7.44 Solve Prob. 7.43 knowing that P = 3wa. 7.45 Assuming the upward reaction of the ground on beam AB to be uni- formly distributed, (a) draw the shear and bending-moment diagrams, (b) determine the maximum absolute values of the shear and bending moment. 7.46 Solve Prob. 7.45 assuming that the 12-kip load has been removed. 7.47 and 7.48 Assuming the upward reaction of the ground on beam AB to be uniformly distributed, (a) draw the shear and bending-moment diagrams, (b) determine the maximum absolute values of the shear and bending moment. 10 kN/m HIe ot —n] Fig. P7.48 10 kN/m ol 200 mm’ | 200 mm ' 200 mm 600 N Fig. P7.49 7.49 Draw the shear and bending-moment diagrams for the beam AB, and determine the shear and bending moment (a) just to the left of C, (b) just to the right of C. c o sn— 4 kips/ft B = L 21t 8 kips D 450 1b 150 Ib/ft esn Fig. P7.42 st | 4] 6kips 12kips Gkips c A Lbsndsnt] 2ft 2ft Fig. P7.45 B 10 kN/m l s c bz s 2] Fig. P7.47

the beam AB, and determine the maximum absolute values of the ll:\n\' llzu\ 120N 7.50 through 7.52 Draw the shear and bending-moment diagrams for shear and bending moment. 200 mm | 200 mm \ 200 mm ‘ Fig. P7.50 1.5 kips. — 0.8 ft dy A i T T ain.L " T Fig. P7.51 Fig. P7.52 Two small channel sections DF and EH have been welded to the uni- form beam AB of weight W = 3 kN to form the rigid structural mem- ber shown. This member is being lifted by two cables attached at D and E. Knowing that 6 = 30° and neglecting the weight of the chan- nel sections, (a) draw the shear and bending-moment diagrams for beam AB, (b) determine the maximum absolute values of the shear and bending moment in the beam. TG 254 Solve Prob. 7.53 when 0 = 60°. —15 m——l—l m»Ll m»l—l.fi m—] For the structural member of Prob. 7.53, determine (a) the angle 6 Fig. P7.53 for which the maximum absolute value of the bending moment in beam AB is as small as possible, (b) the corresponding value of |M|max. (Hint: Draw the bending-moment diagram and then equate the absolute values of the largest positive and negative bending moments obtained.) For the beam of Prob. 7.43, determine (a) the ratio k = P/wa for which the maximum absolute value of the bending moment in the beam is as small as possible, (b) the corresponding value of M|, (See the hint for Prob. 7.55.) Determine (a) the distance for which the maximum absolute value of the bending moment in beam AB is as small as possible, (b) the cor- responding value of [M],s. (See the hint for Prob. 7.55.) 100 100 I I I P C D rE— R Ly E F Dimensions in mm Fig. P7.57

Problems SkN 7.63 Using the method of Sec. 7.3, solve Prob. 7.29. l l l l l l l T l 1 l 1 7.64 Using the method of Sec. 7.3, solve Prob. 7.30. Y BERREE o 7.65 Using the method of Sec. 7.3, solve Prob. 7.31. Czfe ‘50_4 m‘,‘A; 08m— 7.66 Using the method of Sec. 7.3, solve Prob. 7.32. Fig. P7.69 7.67 Using the method of Sec. 7.3, solve Prob. 7.33. 24N 24N 12N 768 Using the method of Sec. 7.3, solve Prob. 7.34. 7.69 and 7.70 For the beam and loading shown, (a) draw the shear and bending-moment diagrams, (b) determine the maximum absolute val- ues of the shear and bending moment. e e 7.71 Using the method of Sec. 7.3, solve Prob. 7.39. Fig. P7.70 7.72 Using the method of Sec. 7.3, solve Prob. 7.40. 7.73 Using the method of Sec. 7.3, solve Prob. 7.41. 7.74 Using the method of Sec. 7.3, solve Prob. 7.42. 775 and 776 For the beam and loading shown, (a) draw the shear and bending-moment diagrams, (b) determine the maximum absolute val- ues of the shear and bending moment. 2kips 3kips 4 kips 2kips 4kips 6 kip-ft 12 kip-ft 5 kip-ft A 1B | - et fi I»sfiakfiflA«sfial Fig. P7.75 Fig. P7.76 7.77 and 7.78 For the beam and loading shown, (a) draw the shear and bending-moment diagrams, () determine the magnitude and location of the maximum absolute value of the bending moment. 36 kN-m 15 kN/m 30 kN-m 90 kN-m LT Fig. P7.77 Fig. P7.78

7.79 and 7.80 For the beam and loading shown, (@) draw the shear and bending-moment diagrams, (5) determine the magnitude and location of the maximum absolute value of the bending moment. 8 kN/m 3, y_L 2 24m— 08m Fig. P7.79 7.81 and 7.82 For the beam and loading shown, (@) draw the shear and bending-moment diagrams, (b) determine the magnitude and location of the maximum absolute value of the bending moment. 250 Ib/ft A 0000 &= A 1250 1b o Fig. P7.81 7.83 (a) Draw the shear and bending-moment diagrams for beam AB, (b) determine the magnitude and location of the maximum absolute value of the bending moment. 300 Ib/ft A - B e @ F- ), pr— I 21t 2ft 300 1b Fig. P7.83 7.84 Solve Prob. 7.83 assuming that the 300-Ib force applied at D is directed upward. 7.85 and 7.86 For the beam and loading shown, (a) write the equations of the shear and bending-moment curves, (b) determine the magnitude and location of the maximum bending moment. w w=wycos > 2L Fig. P7.85 2 kN/m T Fig. P7.80 3200 b 400 Ib/ft T B 251t c Fig. P7.82

7.87 and 7.88 For the beam and loading shown, (a) write the equations of the shear and bending-moment curves, (b) determine the magnitude and location of the maximum bending moment. 21 X W = W Sin — L 1, ~ | Fig. P7.88 Fig. P7.87 7.89 The beam AB supports the uniformly distributed load of 1000 N/m and two unknown forces P and Q. Knowing that it has been experi- mentally determined that the bending moment is —395 N-m at A and —215 N-m at C, (a) determine P and Q, (b) draw the shear and bending-moment diagrams for the beam. 1000 N/m LT A c I** 02 m—{=—02m—{=—0.25 m — Fig. P7.89 7.90 Solve Prob. 7.89 assuming that the uniformly distributed load of 1000 N/m extends over the entire beam AB. *7.91 The beam AB is subjected to the uniformly distributed load of 2 kips/ft and two unknown forces P and Q. Knowing that it has been exper- imentally determined that the bending moment is +172 kip-ft at D and +235 kip-ft at E, (a) determine P and Q, (b) draw the shear and bending-moment diagrams for the beam. 2 kips/ft ITIITL A D B ot l D E l A P’ 1 ft Q I 5 1f— ~3ft fi l—a f— Fig. P7.91 *7.92 Solve Prob. 7.91 assuming that the uniformly distributed load of 2 kips/ft extends over the entire beam AB.