In static, a body is said to be in equilibrium when the force system acting upon it has a zero resultant.
 

Conditions of Static Equilibrium of Concurrent Forces

The sum of all forces in the x-direction or horizontal is zero.

The sum of all forces in the y-direction or vertical is zero.

Important Points for Equilibrium Forces

Problem 271
The three forces in Fig. P-270 create a vertical resultant acting through point A. If T is known to be 361 lb, compute the values of F and P.
 

Problem 270
The three forces shown in Fig. P-270 are required to cause a horizontal resultant acting through point A. If F = 316 lb, determine the values of P and T. Hint: Apply M_R = ΣM_B to determine R, then M_R = ΣM_C to find P, and finally M_R = ΣM_D or R_y = ΣY to compute T.
 

Problem 269
Repeat Prob. 268 is the resultant is 390 lb directed down to the right at a slope of 5 to 12 passing through point A. Also determine the x and y intercepts of the missing force F.
 

Problem 268
The resultant of four forces, of which three are shown in Fig. P-268, is a couple of 480 lb·ft clockwise in sense. If each square is 1 ft on a side, determine the fourth force completely.
 

Problem 267
The Howe roof truss shown in Fig. P-267 carries the given loads. The wind loads are perpendicular to the inclined members. Determine the magnitude of the resultant, its inclination with the horizontal, and where it intersects AB.
 

Problem 266
Determine the resultant of the three forces acting on the dam shown in Fig. P-266 and locate its intersection with the base AB. For good design, this intersection should occur within the middle third of the base. Does it?
 

Problem 265
Compute the resultant of the three forces shown in Fig. P-265. Locate its intersection with X and Y axes.
 

Problem 264
Completely determine the resultant with respect to point O of the force system shown in Fig. P-264.
 

Problem 263
Determine the resultant of the force system shown in Fig. P-263 and its x and y intercepts.