2.1) The support reactions are calculated now: [tex]A_{x} = 10\,kN[/tex], [tex]A_{y} = -10\,kN[/tex], [tex]B_{y} = 30\,kN[/tex].
2.2) The member CD is on tensile load and the member BC is on compressive load. [tex]F_{BC} \approx 28.284\,kN[/tex], [tex]F_{CD} = 20\,kN[/tex]
How to analyze a system in static condition
The dynamic situation of a mechanical system whose geometry cannot be neglected is described by Newton's laws and D'Alembert's principle. A planar system in equilibrium is described by the following formulae:
[tex]\sum F_{x} = 0[/tex] (1)
[tex]\sum F_{y} = 0[/tex] (2)
[tex]\sum M = 0[/tex] (3)
2.1) The support reactions can be found by assuming that the truss is a rigid solid:
[tex]\sum F_{x} = A_{x} - F = 0[/tex] (4)
[tex]A_{x} = F[/tex]
[tex]A_{x} = 10\,kN[/tex]
[tex]\sum M_{A} = F\cdot r_{BD} - G \cdot (r_{AB}+r_{CD}) + B_{y}\cdot r_{AB} = 0[/tex] (5)
[tex]B_{y} = \frac{G\cdot (r_{AB}+r_{CD})-F\cdot r_{BD}}{r_{AB}}[/tex]
[tex]B_{y} =\frac{(20\,kN)\cdot (8\,m)-(10\,kN)\cdot (4\,m)}{4 \,m}[/tex]
[tex]B_{y} = 30\,kN[/tex]
[tex]\sum F_{y} = A_{y} + B_{y} - G = 0[/tex] (6)
[tex]A_{y} = G - B_{y}[/tex]
[tex]A_{y} = 20\,kN - 30\,kN[/tex]
[tex]A_{y} = -10\,kN[/tex]
Note - The negative sign means that the real direction of the component is antiparallel to the assumed one.
2.2) If the entire system is at equilibrium, then every part of the system must be also at equilibrium. The joint is considered a particle and thus the D'Alembert's principle is not necessary. The member CD is on tensile load and the member BC is on compressive load.
[tex]\sum F_{x} = F_{BC} \cdot \cos 45^{\circ} - F_{CD} = 0[/tex] (7)
[tex]\sum F_{y} = -G + F_{BC}\cdot \sin 45^{\circ} = 0[/tex] (8)
By (8):
[tex]F_{BC} = \frac{G}{\sin 45^{\circ}}[/tex]
[tex]F_{BC} \approx 28.284\,kN[/tex]
By (7):
[tex]F_{CD} = F_{BC}\cdot \cos 45^{\circ}[/tex]
[tex]F_{CD} = 20\,kN[/tex]
To learn more on trusses, we kindly invite to check this: https://brainly.com/question/16757156
#SPJ1
