Summary: Resultant & Equilibrium of Force System (Non - Coplanar) | Civil Engineering Optional Notes for UPSC PDF Download

Representation of Force 

There are two ways of representation of force. The method used depends on the type of problem being solved and the easiest approach to finding a solution.

1. Scalar Notation

2. Vector Notation

Vector Notation Of Forces 

1. Two Dimensional Force Systems (Coplanar Forces) It is also possible to represent the x and y components of a force in terms of Cartesian unit vectors i and j.

where the scalars Fx and Fy are the x and y scalar components of the vector F.

2. Three Dimensional Force Systems(Non-Coplanar Forces)

PROBLEMS

1. A force vector F = 700i + 1500j is applied to a bolt. Determine the magnitude of force and the angle it forms with the horizontal.

2. A force of 500 N forms angles 60⁰, 45⁰ and 120⁰ respectively with x, y and z axes. Write the vector form of force.

A. RESULTANT OF NON COPLANAR FORCES -By Vector Notation 

1. Resultant of Non Coplanar Concurrent Forces

In vector notation, the scalar components of the resultant vector can be obtained by adding algebraically the sum of the corresponding scalar components of the force vectors.

where

B. MOMENT AND COUPLE – In Vector Notation 

Moment 

Moment is a vector quantity whose direction is perpendicular to the plane of the body. The right-hand rule is used to establish the sense of direction of moment.
Vector Formulation

Varignon’s Theorem

Vector Formulation 

Couple 

Vector Formulation

Couple vectors are free vectors, i.e., the point of application is not significant.

C. EQUILIBRIUM OF NON COPLANAR FORCES – By Vector Notation

1. Equilibrium of Non-Coplanar Concurrent Forces 

In vector notation, the equation of equilibrium can be summarized as