Presentation of Forces Resolution II

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







Forces Resolution

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







Forces Resolution
The effect of a single force can be replaced by the effects of several components (forces).
Force f shown below can be resolve into two perpendicular components (the angle between the components is equal to 90o ) fx and fy:



In this case using Parallelogram Law:
f_x=f×cos??
f_y=f×sin??
f=?(f_x^2+f_y^2 )
?=tan^(-1)??(f_y/f_x ?)
The effect of the original force (f) is equivalent to the combination effects of forces f_x and f_y.
If the force (f) is in space with ?_x, the angle between the force f and x-axes, ?_y, the angle between the force f and y-axes and ?_z, the angle between the force f and z-axes.
using Parallelogram Law:
f_x=f×cos???_x ?
f_y=f×cos???_y ?
f_z=f×cos???_z ?
f=?(f_x^2+f_y^2+f_z^2 )
The effect of the original force (f) is equivalent to the combination effects of forces f_x, f_y and f_z.

If the angle between the two components is not perpendicular (90o), the sine law of the parallelogram law is applicable:











Then
R=?(?F_1?^2+?F_2?^2+2F_1 F_2 cos?? )
Apply triangle law:
R/sin?(180-?) =F_1/sin?? =F_2/sin??
Force Sign Convention













Applications

Problem1:
Find the perpendicular components (F_x,F_y) of the external force P = 1 kN that are applied on the concrete beam shown below:



Solution:




f_x=P×cos???=1×cos??30=0.86kN?? ?
f_y=P×sin??=1×sin??30=0.5kN??
For the checking purpose
P=?(f_x^2+f_y^2 )=?(?0.86?^2+?0.5?^2 )=0.995kN?1kN
?=tan^(-1)??(f_y/f_x ?)=tan^(-1)??(0.5/0.86?)=30.17°?30°