Step 1: Analyze the overall equilibrium of the truss.
For the truss to be in equilibrium, the sum of horizontal forces, vertical forces, and moments must be zero.
Step 2: Calculate the horizontal and vertical reactions at supports A, L, and K.
∑Fx=0⇒Ax−10 kN+Lx=0
∑Fy=0⇒Ay+Ly+Ky−10 kN=0
Step 3: Calculate the moments about point A to find
Ky.
∑MA=0⇒10 kN×6 m+10 kN×1 m−Ky×7 m−Ly×6 m=0
Assuming
Ly=Ky for simplicity (since there's no horizontal displacement at K and no other horizontal forces acting between L and K),
70 kN⋅m=Ky×7 m+Ly×6 m
70=13Ky⇒Ky≈5.38 kN
Ly=70−5.38×7÷6≈7.5 kN
Step 4: Conclude the support reaction at L.
Ly≈7.5 kN