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Horizontal Force Is Equal To = 600 N
Acting angle to the horizontal is equal = 46ยบ or
degrees.
Fx = 600 x Cos(46)
Fy = 600 x Sin(46)
Fx = 600 x 0.694425881510006
Fy = 600 x 0.719564239723634
Fx = 416.655528906003
Fy = 431.73854383418
Fx = 416.66 N
Fy = 431.74 N
The rectangular weight/body is = 500 N/M
The triangular weight/body is = 400 N/M
Area of a rectangle = Length x Width = (LW) and area
of a triangle = (base x Height) / 2 ) = bh/2)
Total legth of the beam/body = 13.5 M and the
midpoint is = 6.75 M
F1 (From the rectangular weight) = (500 X 13.5)
F2 (From the triangular weight) = ( 400 x 13.5 / 2)
F1 (From the rectangular weight) = 6750
F2 (From the triangular weight) = 2700
F1 (From the rectangular weight) = 6,750.00 N
F2 (From the triangular weight) = 2,700.00 N
F2 is distance from the left side is = 2 / 3 x 13.5N
F2 is distance from the left side is = 9M
F2 is distance from the right side is = 4.5M
Sum of the forces in X direction is equla to zero.
--> + F(X) = 0
Ax - 416.66 = 0 Eqn.(1)
Ax = 416.66
Ax = 416.66 N
Sum of the forces in Y direction is equla to zero.
/\ + F(y) = 0
|
Ay + By - 431.74 - 6750 - 2700 = 0 Eqn.(2)
Ay + By = 9881.74 eqn.(2)
Sum of the moment at A is equla to zero.
From Left side/hand to the right is positive.
L--> + M(A) = 0
-1 x 6 x 431.74 - 6.75 x 6750 - 9 x 2700 + 13.5 x By
= 0 Eqn.(3)
13.5By = 2590.44 + 45562.5 + 24300 = 0 Eqn.(3)
13.5By = 72452.94 By = 72452.94 / 13.5
By = 5366.88444444444
By = 5366.88 N
From Eqn.(2)
Ay + By = 9881.74 eqn.(2)
Ay = 9881.74 - By eqn.(2)
Ay = 9881.74 - 5366.88
Ay = 4514.86
Ay = 4514.86 N
Sum of the moment at B is equla to zero.
From Right side/hand to the left is positive.
<--I + M(B) = 0
4.5 x 2700 + 6.75 x 6750 + 7.5 x 431.74 - 13.5 x Ay
Flavour ft. Tiwa Savage - Oyi Remix.mp3
= 0 Eqn.(4)
60950.55 - 13.5 x Ay = 0 Eqn.(4)
13.5Ay = 60950.55
Ay = 60950.55 / 13.5
Ay = 4514.85555555556
Ay = 4514.86
Ay = 4514.86 N
Likewise, we can use the formula for the area of
Parallelogram
to determine the total weight of the shape on the
beam/body.
Area of Parallelogram = 1/2[A+B] x h
A = 500 + 400 ; B = 500 ; h = 13.5
A = 900 ; B 500 ; h = 13.5
Area = 1 / 2 x [ 900 + 500 ] x 13.5
Area = Total Weight = 9450
Area = Total Weight = 9,450.00 N
Ay + By = 9450 + 431.74
Ay + By = 9881.74 Eqn.(5)
The last thing to consider is to take moment about
point C of the beam/body for our last consideration.
L--> + M(C) = 0
6 x -Ay + 7.5 x By - 0.75 x 6750 - 3 x 2700 = 0 Eqn.(6)
-6Ay + 7.5By = 5062.5 + 8100 Eqn.(6)
-6Ay + 7.5By = 13162.5 Eqn.(6)
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From Eqn.(5) and Eqn.(6) above
Ay + By = 9881.74 Eqn.(5)
-6Ay + 7.5By = 13162.5 Eqn.(6)
Solve Eqn.(5) and Eqn.(6) using Matrices
| Ay By |
| 1 1 | 9881.74 | Eqn.(5)
| -6 7.5 | 13162.5 | Eqn.(6)
Det. = 1 x 7.5 - -6 x 1
Det. = 7.5 + 6
Det. = 13.5
Ay =
| 9881.74 1 |
| 13162.5 7.5 |
Ay = 9881.74 x 7.5 - 13162.5 x 1
Ay = 74113.05 - 13162.5
Ay = 60950.55
Ay = 60950.55 / 13.5
Ay = 4514.86
Ay = 4514.86 N
By =
| 1 9881.74 |
| -6 13162.5 |
By = 1 x 13162.5 - -6 x 9881.74
By = 13162.5 - -59290.44
By = 72452.94
By = 72452.94 / 13.5
By = 5366.88
By = 5366.88 N
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