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7 1 Determine the internal normal force and shear force and the bending moment in the beam at points C and D Assume the support at B is a roller Point C is located just to the right of the 8 kip load 8 kip 40 kip ft A C 8 ft D 8 ft B 8 ft SOLUTION Support Reactions FBD a a MA 0 c Fy 0 By 24 40 8 8 0 Ay 1 00 8 0 F 0 x By 1 00 kip Ay 7 00 kip Ax 0 T an his th d wo sa eir is p rk w le co ro is ill o u vi pr de f a rse de ot st ny s d s ec ro p an o te y ar d le d th t o a ly by e s in f th se for Un te is ss th ite gr w in e ity o g us d S of rk stu e o tat th inc de f i es e lu nt ns co w d le tr p or in a uc y k g rn to rig an on in rs h d th g in t la is e D t w no W iss ea s t p or em ch in er ld m W ina g itt id tio ed e n We or b Internal Forces Applying the equations of equilibrium to segment AC FBD b we have F 0 x c Fy 0 a MC 0 NC 0 7 00 8 VC 0 MC 7 00 8 0 VC 1 00 kip MC 56 0 kip ft Ans Ans Ans Applying the equations of equilibrium to segment BD FBD c we have F 0 x c Fy 0 a MD 0 VD 1 00 0 ND 0 VD 1 00 kip Ans Ans 1 00 8 40 MD 0 MD 48 0 kip ft Ans 2013 Pearson Education Inc Upper Saddle River NJ All rights reserved This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction storage in a retrieval system or transmission in any form or by any means electronic mechanical photocopying recording or likewise For information regarding permission s write to Rights and Permissions Department Pearson Education Inc Upper Saddle River NJ 07458 7 2 Determine the shear force and moment at points C and D 500 lb 300 lb 200 lb B A C 6 ft 4 ft E D 4 ft 6 ft 2 ft SOLUTION Support Reactions FBD a a MB 0 500 8 300 8 Ay 14 0 Ay 114 29 lb Internal Forces Applying the equations of equilibrium to segment AC FBD b we have NC 0 114 29 500 VC 0 c Fy 0 a MC 0 Ans T an his th d wo sa eir is p rk w le co ro is ill o u vi pr de f a rse de ot st ny s d s ec ro p an o te y ar d le d th t o a ly by e s in f th se for Un te is ss th ite gr w in e ity o g us d S of rk stu e o tat th inc de f i es e lu nt ns co w d le tr p or in a uc y k g rn to rig an on in rs h d th g in t la is e D t w no W iss ea s t p or em ch in er ld m W ina g itt id tio ed e n We or b F 0 x VC 386 lb Ans MC 500 4 114 29 10 0 MC 857 lb ft Ans Applying the equations of equilibrium to segment ED FBD c we have F 0 x c Fy 0 a MD 0 ND 0 VD 300 0 MD 300 2 0 Ans VD 300 lb Ans MD 600 lb ft Ans 2013 Pearson Education Inc Upper Saddle River NJ All rights reserved This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction storage in a retrieval system or transmission in any form or by any means electronic mechanical photocopying recording or likewise For information regarding permission s write to Rights and Permissions Department Pearson Education Inc Upper Saddle River NJ 07458 7 3 The strongback or lifting beam is used for materials handling If the suspended load has a weight of 2 kN and a center of gravity of G determine the placement d of the padeyes on the top of the beam so that there is no moment developed within the length AB of the beam The lifting bridle has two legs that are positioned at 45 as shown 3m d A 3m 45 45 B d 0 2 m 0 2 m SOLUTION E F Support Reactions From FBD a a ME 0 FF162 2132 0 FE 1 00 kN c Fy 0 FF 1 00 2 0 FF 1 00 kN G From FBD b c Fy 0 FAC cos 45 FBC cos 45 0 FAC FBC F 2F sin 45 1 00 1 00 0 T an his th d wo sa eir is p rk w le co ro is ill o u vi pr de f a rse de ot st ny s d s ec ro p an o te y ar d le d th t o a ly by e s in f th se for Un te is ss th ite gr w in e ity o g us d S of rk stu e o tat th inc de f i es e lu nt ns co w d le tr p or in a uc y k g rn to rig an on in rs h d th g in t la is e D t w no W iss ea s t p or em ch in er ld m W ina g itt id tio ed e n We or b F 0 x FAC FBC F 1 414 kN Internal Forces This problem requires MH 0 Summing moments about point H of segment EH FBD c we have a MH 0 1 001d x2 1 414 sin 45 1x2 1 414 cos 45 10 22 0 d 0 200 m Ans 2013 Pearson Education Inc Upper Saddle River NJ All rights reserved This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction storage in a retrieval system or transmission in any form or by any means electronic mechanical photocopying recording or likewise For information regarding permission s write to Rights and Permissions Department Pearson Education Inc Upper Saddle River NJ 07458 7 4 The boom DF of the jib crane and the column DE have a uniform weight of 50 lb ft If the hoist and load weigh 300 lb determine the normal force shear force and moment in …
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