Question

A mass of 500 kg is suspended from a beam by two chains 1,5 m and 2,7 m long respectively. The distance between the suspension points is 3,746 m (see Fig. 5). Determine (a) the load in each chain; the vertical and horizontal reactions at the suspension points. (b) -3,746 m 8746 900 m 500 kg

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Answer 1

SIME solution 3.746 A Date - Page r . 7 m Usiry law of cosines. (2.7)² = 1.5² +3.746 = 2x1.5x3.746 Cos ac Cosa = 0.8002 - loc = 36-8521 I using sine Rule. Sire a = Sin ß 2. 7 1.5 sinB = 1.5xsin 36.852 2.7. TB = 19.4631 + 8 = 180-836.852719.467? h = 123.685 | IFBO of point © By Lani's thomem. 1 x 7.688 , XB-19.463 1 - 12 0 0x9.81 asian Sin 109.463 sin 126.852 Sin 123.685 I 50049.81 T= 500 x 9.81 Sin 123.685 x Sin109.463 5557.89 N.

Tz=500x9.81 Sik 123.685 -X sin126.852 classmate Date page =4716.88 N. - Horizontal freutical Reaction at 'A 1 Sin 36.852 - 5557.89% sim 36.852 IVA = 33 33.34 N. HA=Ti Cos 36.852 THA = 4447.35 h.) Howzontal & venticos components at B VA = Tz simß = 4716.88X 5in 19.463 B = 1571.66 N. HA = Te Cos 19.463 F = u F16.88 x Cos 19.463 H3 = 4447.35N)

solution (2) czon! classmate 20N Dote page Eta= 10 60530 + 2000s lo° +30 Cos30° { fn = 54.337 M. losin 30 Efy = 10 +3osir 30 + 2o sinlo Efy = 23.473. N. Resultat = 1 18.² + ({fyj? R $4.337] + (23-473)? R = 59.19.0 Ans. tano = {fy Efn. o = tant 23.473 54.337 To = 23.36° { from the x-aris} Am

JOON + 325 4 solution (3) classmate Date F Page - AB 900 Equilibrium of forces in Z-direction R,+R2 + Rz = 500 N Em about 2-axis = 0. 360 X 3 - 2 x +2, x = 0 & m about y-axis = 0. -50076 - RzXO-R₂ x 0 =0 - Firding <A wing law of Cosines. Los A = 900² +6252 3252 2 19.0) (625) Cosa = 7 ZA = 13.26 => 30-A = 46.76 & B = 625 sin(16.74) 1B = 180 mor. c = 625 Cos 16.74 1 = 598.5 mm D = 900 Corso T & 10 - 779.4 mm

I putting values in 1,24 3. we get I 500 x 180 – Rz x 450 + R₂X450=0 R₃-R2 = 200 classmate Date Page In 2 500 x 598.5 = R2 + R3) 779.4 R2 + R3 = 38319 - Solving 4 4 we get to R3=291.97 N 12, - 9 7 và 4 R = 500-{291.97+91-971 Army R, = 1/5 06 N|

classmate Solution (4) Date FOON Page Horizontal component th= 100 Cosgoo OYO 86.60 N Vertical Component. fv = 100 sin 300 Fu = 50 H