Find one or two unknown cable or member forces at a point using horizontal and vertical equilibrium, with worked steps and sign conventions.
Direct solving is free and needs no account. Have a word problem instead? Submit it as text.
Worked examples
These are the solver's own reference problems — the answers come from published sources or independent hand computation, never from the solver itself. The solution below is the live solver output for each.
Example 1
symmetric cables at 30° and 150° holding 100 N
Given
known forces
1.magnitude 100 Nangle deg 270
unknown directions
1.angle deg 30
2.angle deg 150
Assumptions
All forces are concurrent and coplanar; members are two-force (axial) so their force acts along their direction; positive = tension.
Solution steps
Sum the known forces
Everything already known collapses into one net force the unknowns must balance.
ΣFx = 0 and ΣFy = 0
Known net: Fx = -1.837e-17 kN, Fy = -0.1 kN
Solve for member 1
The member's force component balance along x and y fixes its magnitude.
each T acts along its member direction
0.1 kN at 30° (tension)
= 0.1 kN
Solve for member 2
The member's force component balance along x and y fixes its magnitude.
each T acts along its member direction
0.1 kN at 150° (tension)
= 0.1 kN
Results
Force in member 1 (positive = tension)
0.1kN
Force in member 2 (positive = tension)
0.1kN
Where this answer was checked
source
ΣFx = ΣFy = 0, symmetric case — equal tensions of 100 N
verified by
hand-recomputed
derivation
Symmetry gives T1 = T2 = T. Vertical: 2·T·sin30° = 100 → T = 100 N.
Example 2
asymmetric cables at 45° and 120° holding 200 N
Given
known forces
1.magnitude 200 Nangle deg 270
unknown directions
1.angle deg 45label cable AB
2.angle deg 120label cable AC
Assumptions
All forces are concurrent and coplanar; members are two-force (axial) so their force acts along their direction; positive = tension.
Solution steps
Sum the known forces
Everything already known collapses into one net force the unknowns must balance.
ΣFx = 0 and ΣFy = 0
Known net: Fx = -3.674e-17 kN, Fy = -0.2 kN
Solve for cable AB
The member's force component balance along x and y fixes its magnitude.
each T acts along its member direction
0.1035 kN at 45° (tension)
= 0.1035 kN
Solve for cable AC
The member's force component balance along x and y fixes its magnitude.