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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.

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Answer:

[tex]R= 337.75\ \bar i - 2275 \ \bar j \ \ N[/tex]

[tex]\sum M_A = -13650 \ N.m[/tex]

x = 6 m

Explanation:

From the diagram attached below :

Equivalent force:

[tex]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[/tex]

[tex]R= 337.75\ \bar i - 2275 \ \bar j \ \ N[/tex]

The equivalent couple at point A is as follows:

[tex]\sum M_A = -390(3)-520(\frac{6}{2})- 520({6})- 520(6+\frac{6}{2}) -260(12)[/tex]

[tex]\sum M_A = -13650 \ N.m[/tex]

By applying the principles of momentum :

[tex]\sum M_A = Ry(x)[/tex]

[tex]- 13650 = - 2275 \ x[/tex]

x = [tex]\frac{13650}{2275}[/tex]

x = 6 m

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