Presentation of Resultant of a Cunccurent, Coplanar Force System II

University of Babylon
College of Engineering
Department of Environmental Engineering
Engineering Analysis I (ENAN 103)







Resultant of a Cunccurent, Coplanar Force System

Undergraduate Level, 1st Stage



Mr. Waleed Ali Tameemi
College of Engineering/ Babylon University
M.Sc. Civil Engineering/ the University of Kansas/ USA



2016-2017

Course Outline
Introduction
Parallelogram Law
Forces Resolution
Resultant of a Cunccurent, Coplanar Force System
Moment (Moment of a Force)
Couples
Resultant of a Non-concurrent, Coplanar Force System
Resultant of a Concurrent Non-coplanar Force System
Equilibrium
Fraction
Truss
Method of Joints
Method of Sections








Resultant of a Cunccurent, Coplanar Force System
The resultant of this system is a single force that pass through the point of concurrence.
In order to calculate the resultant magnitude and direction, the following procedure is required:




Resolve each single force to its perpendicular components.




f_x=f×cos??
f_y=f×sin??
p_x=p×cos??
p_y=p×sin??
Calculate the resultant’s components in x direction and y direction.
R_x=f_x+p_x
R_y=f_y+p_y
Calculate the magnitude of the resultant.
R=?(R_x+R_y )
Calculate the resultant’s slope.
tan^(-1)??(R_y/R_x ?)
Applications
Problem 1:
For the concurrent, coplanar force system, calculate the magnitude and the slope of its resultant.






Solution:
Resolve each single force to its perpendicular components of each force.













f_x=100×cos??30=+86.6 N??
f_y=100×sin??30=+50 N ??
p_x=150×cos?45=-106.1 N=101.1 N ?
p_y=150×sin?45=+106.1 N ?
T_x=50×cos?90=zero
T_y=50×sin?90=-50 N=50 N ?

Calculate the resultant’s components in x direction and y direction.
R_x=f_x+p_x+T_x=86.6-106.1+0=-19.5 N=19.5 N ?
R_y=f_y+p_y+T_y=50+106.1-50=+106.1 N ?
Calculate the magnitude of the resultant.
R=?(R_x+R_y )=?(?19.5?^2+?106.1?^2 )=107.9 N
Calculate the resultant’s slope.
tan^(-1)??(106.1/19.5?)=79.6°