PROBLEMS. m s TAC. m = 60 kg/m, determine the tension in the two supporting cables and the reaction at D.

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2 1. he uniform I-beam has a mass of 60 kg per meter of its length. Determine the tension in the two supporting cables and the reaction at D. (3/62)

3 A( 500) m (5 23) m m = 60 kg/m determine the tension in the two supporting cables and the reaction at D. C (523) m D (000) m G (300) m 2 3k A A k A G 2 3k W D k D Dk kg W 60 8m 9.81 m k k ( ) 2 m s M A 0 rg / AW rd / A D 0 i k i k D D D

4 A( 500) m (5 23) m m = 60 kg/m determine the tension in the two supporting cables and the reaction at D. C (523) m D (000) m G (300) m A A k k A W G D F 0 A F 0 2(0.83) A A

5 2. A 36 kg sheet of plwood rests on two small wooden blocks as shown. It is allowed to lean 20 from the vertical under the action of a force P which is perpendicular to the sheet. Friction at all surfaces of blocks A and is sufficient to prevent slipping. Determine the magnitude P and the vertical reaction forces at A and. (3/64)

6 m = 36 kg. Friction at all surfaces of blocks A and is sufficient to prevent slipping. Determine the magnitude P and the vertical reaction forces at A and.

7 3. he light right-angle boom which supports the 400 kg clinder is supported b three cables and a ball and socket oint at attached to the vertical - surface. Determine the reactions at and the cable tensions. (3/73)

8 oom is supported b three cables and a ball and socket oint at. Determine the reactions at and the cable tensions. A( 002) m (1.502) m C ( 110) m D E D i 2k i k 2 2k E k k i k W 400(9.81) 3924 ( ) (000) m W D(1.520) m E (1.500) m G (0.7502) m G D E

9 i k E E D D D (2775) PRLEMS D E W G i k i k i E D D D k i D E D D m G m E m D m m C m m A (0.7502) (1.500) (1.520) (000) 110) ( (1.502) 002) ( / / / k k k i k i k i k r W r r M E D E D G A

10 oom is supported b three cables and a ball and socket oint at. Determine the reactions at and the cable tensions. F F D 0 F D E D E G W

11 4. he uniform panel door has a mass of 30 kg and is prevented from opening b the strut C which is a light two-force member whose upper end is secured under the door knob and whose lower end is attached to a rubber cup which does not slip on the floor. f the door hinges A and onl can support force in the vertical -direction. Calculate the compression C in the strut and the horiontal components of the forces supported b hinges A and when a horiontal force P = 200 is applied normal to the plane of the door as shown. (3/89)

12 of the door hinges A and onl can support force in the vertical - direction calculate the compression C in the strut and the horiontal components of the forces supported b hinges A and (0 0 0) A ( ) ( ) G ( ) E (0 0 2) D ( ) H ( ) m 0.75 k ndh k 1.25 FC FC ndh FC k A Ai A i k W 30(9.81) k 294.3k P 200 M M M 0 0.6i 0.8k 294.3k i 0.8k F C k i k k A i A 0.48F 1.6A 360i 0.8F 1.6A F 240k C C P E D F C C G A W H A

13 of the door hinges A and onl can support force in the vertical -direction calculate the compression C in the strut and the horiontal components of the forces supported b hinges A and k i 0.6F 0.48F 1.6A C C A 0.8F A C F C A A P E D F C G A W A F F 0 0 A A F A C H

14 5. Consider the rudder assembl of a radio controlled model airplane. For the 15 position shown in the figure the net pressure acting on the left side of the rectangular rudder area is p = 4(10-5 ) /mm 2. Determine the required force P in the control rod DE and the horiontal components of the reactions at hinge which are parallel to the rudder surface. Assume the aerodnamic pressure to be uniform. (3/92)

15 P Pi A A i A p = 4(10-5 ) /mm 2 determine P and horiontal components of reaction at parallel to rudder surface. A k i k 2 Area of rudder A mm F pa410 F 0.15sin15i 0.15cos i top view of rudder 22 16sin15= F 15 H P H C D C D A cos15= (3840) (000) A(00 26) mm (0068) mm D( ) mm H (24cos15 24sin15 40) ( ) mm F H P A A A

16 PPi p = 4(10-5 ) /mm 2 determine P and horiontal components of reaction at parallel to rudder surface. A A i A A k i k F i M A M AnA M Ak 0 M A rh / AF r / ArD / AP i k i i k Pi i P Pk 0 M k 0 P0.202 (000) A(00 26) mm (0068) mm D( ) mm H ( ) mm 42k i k i A P F A A H A P

17 6. Under the action of the 40 m torque applied to the vertical shaft the restraining cable limits the rotation of the arm A and attached shaft to an angle of 60 measured from the ais. he collar D fastened to the shaft prevents downward motion of the shaft in its bearing. Calculate the bending moment M the compression P and the shear force V in the shaft at section. (ending moment epressed as a vector is normal to the shaft ais and shear force is also normal to the shaft ais.) (3/94)

18 0.1386i k collar D prevents downward motion of the shaft in its bearing calculate the bending moment M the compression P and the shear force V in the shaft at section. (ending moment epressed as a vector is normal to the shaft ais and shear force is also normal to the shaft ais.) A( 0.16sin cos600) ( ) m ( ) m C ( ) m M 40k M 0 rc / i M 40k M 0.53i k 0.09k i k M M i M M k 0 i M M

19 k i F F collar D prevents downward motion of the shaft in its bearing calculate the bending moment M the compression P and the shear force V in the shaft at section. (ending moment epressed as a vector is normal to the shaft ais and shear force is also normal to the shaft ais.) 0.53i k M m M m M M M V m M M F P320.19

20 7. he electric sander has a mass of 3 kg with mass center at G and is held in a slightl tilted position (-ais vertical) so that the sanding disk makes contact at its top with the surface being sanded. he sander is gripped b its handles at and C. If the normal force R against the disk is maintained at 20 and is due entirel to the force component (i.e. C = 0) and if the friction force F acting on the disk is 60 percent of R determine the components of the couple M which must be applied to the handle at C to hold the sander in position. Assume that half of the weight is supported at C. (3/95)

21 m =3 kg normal force R =20 due entirel to force component (i.e. C = 0) the friction force F acting on the disk 60 percent of R determine the components of the couple M which must be applied to the handle at C to hold the sander in position. Assume that half of the weight is supported at C. 20 F M C M i M C 0 r / C M k 0 A( ) m ( ) m C (00300) m G ( 400 0) m R = 20 i k r W r Ri F 0 G/ C G/ A C C W M F = 0.6R=12 W = C C 300k 40i i 14.72k 300k 40i 400k 120i 20i 12 M i M M k k M M

22 m =3 kg normal force R =20 due entirel to force component (i.e. C = 0) the friction force F acting on the disk 60 percent of R determine the components of the couple M which must be applied to the handle at C to hold the sander in position. Assume that half of the weight is supported at C. M C M i M M k 0 R = 20 F = 0.6R=12 W = M M M 1856 mm mm 2560 mm C 12 M C C M M

23 8. ecause of friction a ver large force is required to raise the 10 kg bod when the cable is wound around a fied rough clinder as shown. For the static equilibrium values shown determine all of the reactions at point. he 0.3 m dimension refers to the point A where the cable loses contact with the clinder. eglect the weight of the fied clinder.

24 A mm W=10(9.81)=98.1 = k A 60 determine all of the reactions at point neglect the weight of the fied clinder M (0 0 0) A (30sin60 30cos60 800) = ( ) ( ) mm M sin 30 cos k 15 k cos 20 cos30cos 20 sin 20 cos 30sin k 8.89 k M W

25 i k? M M i M M k? M 0 r / W ra / M M k i k 15i k M M M M M determine all of the reactions at point neglect the weight of the fied clinder 0 M i M M k M i M M k kmm i k kmm 19.4 kmm 12.1 km km km km M km M M M W (0 0 0) A ( ) ( ) mm F F F k 8.89 k k 14.9i k k k

26 9. he two bars and CD are homogeneous and weigh 200 /m. Joints A C and D are ball-and-socket oints and a cable is connected between and E. Determine all reactions that act on bar.

27 and CD are homogeneous and weigh 200 /m. Joints A C and D are ball-and-socket oints and a cable is connected between and E. Determine all reactions that act on bar.

28 10. he structure is subected to the loadings shown. Member A is supported b a ball and socket oint at A and a smooth collar at. Member CD is supported b a pin at C which acts like a thrust bearing. Determine the reactions at A and C.

29 all and socket oint at A smooth collar at thrust bearing at C. Determine reactions at A and C.

30 11. A circular plate with a weight of 900 acting at its center point G is supported b cord DE and a thrust bearing at. Shaft is fied and frictionless. Determine the cable tension and the reactions acting on the circular plate from the bearing at. G D G

31 W = 900 circular plate supported b cord DE and a thrust bearing at. Shaft is fied and frictionless. Determine the cable tension and the reactions at bearing. G D G

32 12. wo rods are welded to each other to form a -shaped assembl. End D of the assembl contacts a frictionless vertical wall while the assembl is supported b radial bearings at A and. When the assembl is subected to a vertical 800 load P applied to the midpoint of arm DC determine a) he contact force acting on the assembl from the wall at point D b) Components of the bearing reactions acting at.

33 Determine the contact force acting on the assembl from the frictionless wall at D and components of the bearing reactions acting at.

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