This document discusses concurrent force systems and provides examples of calculating the magnitude and direction of the resultant force for two concurrent force systems. A concurrent force system is one where the lines of action of the individual forces pass through a common point. The document solves two example problems, showing the steps to take the algebraic sum of the horizontal and vertical force components and use those sums to calculate the magnitude and direction of the resultant force using trigonometric functions.

1. ENGINEERING
MECHANICS-
CONCURRENT FORCE
SYSTEM
Prof. VINOD B SHIKHARE
HOD & Assistant Professor
Department of Civil Engineering
ICEEM, Aurangabad

2. Concurrent Force System
If the line of action of forces forming the system passes through
a common point (point of concurrence) then the system is said
to be concurrent.

3. Problem 1
 Find out the magnitude and direction of resultant for the given force
system.

4. Solution:
 1. Algebraic sum of horizontal forces,
∴ ƩH= -75 cos 60 + 65 cos 30 + 55 = 73.80 N
 2. Algebraic sum of vertical forces,
∴ ƩV = 75 sin 60 + 65 sin 30 – 80 = 17.42 N
 3. Magnitude of Resultant = R
= ƩH2 + ƩV2
= (73.80)2+(17.42)2
= 75.82 N

5.  4. Direction of Resultant = θ
= tan-1
(ƩV)
(ƩH)
= tan-1
(17.42)
(73.80)
= 13.280
Answer: Magnitude of Resultant =R = 75.82 N &
Direction of Resultant = θ = 13.280

6. Problem 2
 Find out the magnitude and direction of resultant for the given force
system.

7. Solution:
 1. Algebraic sum of horizontal forces,
∴ ƩH= 400 cos 50 + 500 cos 60 - 200 = 307.11 N
 2. Algebraic sum of vertical forces,
∴ ƩV = 400 sin 50 - 500 sin 60 + 300 = 173.40 N
 3. Magnitude of Resultant = R
= ƩH2 + ƩV2
= (307.11)2+(173.40)2
= 352.68 N

8.  4. Direction of Resultant = θ
= tan-1
(ƩV)
(ƩH)
= tan-1
(173.40)
(307.11)
= 29.440
Answer: Magnitude of Resultant =R = 352.68 N &
Direction of Resultant = θ = 29.440

9. Thank You