Question

Find the reaction forces at A and B. A is a pin joint and provides a reaction force in both X and Y. B is a roller joint and provides a reaction force only in the y direction. Please show your work. in both X and Y. Bisa 900 N/m 300 N/m 250 N/m JB 3 m— + 1.5 m --

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Answer 1

Resultant of Distotbuted Lands The resultant of a distributed lood is equal to the area of the load diagram. It is acting at the centroid of that area. 42 | 1/2 R 524/3 /4/3³ TBW 201. EVO - L Rectangular Lood = WL Triangular lood = w2 W2113w2-wi wir - []???///// faiz oidal Load ₃. Wilt 1 (W2-W,DL Resolution into rectangular and triangular loadi 7900N/m 250N/m loads. The trapezoidal load can be Brow/m 0 simplified into combination of rectangular and triangular thit 3m x 15m the Let the resultant for the triangular part be FL It will acte at the mid-point of the rectangular load Fi = 300 x3 = 900 N It acts at 1.5m from the 300N/m VW a A Bm joint

42-17 (erowym Let the resultant force for torongular bad be F2 F2 = 4*3x (900-300) = 900 N LATIMIT 300N/m It acts at a distance 24 from 3m - foint A (2= 3 m) . = 2x3 = 2m Let the resultant for another rectangular load be F3. Fx = 250x1.5 = 375 N It will act at 1.8/2=0.75m 1.5 → away from joint B. Now replacing the distributed loads with their resultant forces we have. srces we Fin F2 F3 13 50N/3 B Rog hatt Roxo 1.5m 75 TTT77 1 .5 3 R Rx , Ry and R are the reaction forces. Summing all the forces acting along horizontal direction = o - Re=0 Suming all the forces acting in vertical direction = 0 - Ry-F,-F -F3+R = 0 = Ry + R = Fi + Fz +F3 - (i)

Summation of for clockwise Taking moment of forces about Joint A = 0 tie ZMA = 0 (positive for counter clockwise and negative => 4.5 R - 1.5F; - 272 - (0.75 +3)Fz = 0 => 4.5R = 1.57,+ 2F2+ 3.75 F2. R 1.5X900 + 2 x 900 + 3.75 X 375 4.5 R = 1012.5 N From equation (é), Ry + R = F + F2 = F3 =2175 ... The Ry - 2175 - R =(2175-1012.5)N = 1162.5 N reaction forces are, Rx=0 Ry = 1162.5 N R = 1012.5 N