Question

The asymmetric roof truss is of the type used when a near normal angle of incidence of sunlight onto the south-facing surface ABC is desirable for solar energy purposes. The five vertical loads represent the effect of the weights of the truss and supported roofing materials. The 390-N load represents the effect of wind pressure. Determine the equivalent force-couple system at A. The couple is positive if counterclockwise, negative if clockwise. Also, compute the x-intercept of the line of action of the system resultant treated as a single force R.

Answer 1

`R= 337.75\ \bar i - 2275 \ \bar j \ \ N`

`\sum M_A = -13650 \ N.m`

x = 6 m

Step-by-step explanation:

From the diagram attached below :

Equivalent force:

`R= -260 \bar j + 390 \ cos 30 \bar{ i} - 390 \ sin 30 \bar j - 520 \ \bar j- 520 \ \bar j- 520 \ \bar j- 260 \ \bar j`

`R= 337.75\ \bar i - 2275 \ \bar j \ \ N`

The equivalent couple at point A is as follows:

`\sum M_A = -390(3)-520((6)/(2))- 520({6})- 520(6+(6)/(2)) -260(12)`

`\sum M_A = -13650 \ N.m`

By applying the principles of momentum :

`\sum M_A = Ry(x)`

`- 13650 = - 2275 \ x`

x =
`(13650)/(2275)`

x = 6 m