Lecture Notes of Resultant of a Non-concurrent, Coplanar Force System

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







Resultant of a Non-concurrent, 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
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 Non-concurrent, Coplanar Force System
The resultant of this system can be a single force or a couple. In order to calculate the resultant magnitude, location, 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 =f_x+p_x
R_y=??F_y =f_y+p_y
Calculate the magnitude of the resultant.
R=?(R_x+R_y )
Find the location of the resultant using the moment law.












???M about A=?
R×d_R=???(F_y×d_f ?)=p_y×d_(p_y )+f_y×d_(f_y )

Calculate the resultant’s slope.
Slope=tan^(-1)??(R_y/R_x ?)
?
Applications
Problem 1:
For the given force system, calculate the magnitude, the location, and the slope of its resultant. (For simplicity neglect the effect of the reactions).





Solution

Resolve each single force to its perpendicular components.
f_x=100×cos?37=79.86 N ?
f_y=100×sin?37=60.18 N ?
p_x=75×cos?30=-64.95 N=64.95 N ?
p_y=75×sin?30=-37.5 N=37.5N ?
?





Calculate the resultant’s components in x direction and y direction.
R_x=??F_x =f_x+p_x=79.86-64.95=14.91 N ?
R_y=??F_y =f_y+p_y=60.18-37.5=22.68 N ?
Calculate the magnitude of the resultant.
R=?(R_x+R_y )=?(?14.91?^2+?22.68?^2 )=27.14 N
Find the location of the resultant using the moment law.









Counter Clockwise CCW (+ ve)

???M about A=?
R_y×d_R=???(F_y×d_f ?)=-p_y×d_(p_y )+f_y×d_(f_y )
22.68×d_R=-37.5×1.5+60.18×2.5
d_R= 4.15 m

Calculate the resultant’s slope.
Slope= ?tan?^(-1)??(R_y/R_x ?)=?tan?^(-1)??(22.68/14.91?)=56.69°