환경재료역학 Chapter 1: Statics

장상식

충남대학교 그린건축연구실(CNUTim)

1.1 Introduction

What is Mechanics?

Field of study on the action of loads and the results of loads applied to a body

Classification of mechanics

Statics: Study on the equilibrium of loads applied to a fixed rigid body

Dynamics: Study on the moving loads and their effects

Mechanics of materials: Study on the action of loads and their results considering the characteristics(deformation) of materials

Structural mechanics: Study on the loads applied to a structure and the resulting deformation

In this semester

Statics: Equilibrium of loads acting on a plane

Mechanics of materials: Loads and deformation within elastic limit

1.2 Concurrent forces in a plane

Terminology Statics: Equilibrium of forces acting on a rigid body

Rigid body: a theoretical body with the assumption that there is no deformation under loads(forces) Rigid body does not exist in this world

However, small deformation under small loads within the elastic limit can be safely ignored.

In statics, all the body are assumed to be rigid

Force(load): Any action resulting changes of the status of a body when applied to that body

Gravity, weight, force, magnetic force, wind force, atmospheric pressure, steam pressure, …

Force: Magnitude, Point of application, Direction

Magnitude – kgf, lbf, N

Point of application – Assume as a concentrated load at a point

Direction – The direction of movement for a body under loads

Line of application – A straight line from the point of application to the direction of a force

Vector: a quantity having direction and magnitude and represented by an arrow

The point of application can be any point on the line of application

Parallelogram of forces: Parallelogram law

c = a + b

Geometric addition: Triangle of forces

c = a + b

If α → 0, then two forces are on a straight line: collinear forces

Equilibrium of collinear forces Addition of collinear forces

c = a + b

For a body in equilibrium, the resultant of forces acting shall be zero

c = a + b = 0 ∴ a = -b (Same magnitude, opposite direction)

Equilibrium law Two forces can be in equilibrium only if they are equal in magnitude, opposite in direction and collinear in action

Intensity of the internal forces, i.e. the force per unit cross sectional area is called as the stress in the bar

(a) = (b) = (c) : Theorem of transmissibility

(a) (b) (c)

Equilibrium of two forces

All bars are in equilibrium

Resultant of two forces

Two forces p and f can be represented by the resultant R

Actions and reactions Restriction to the free motion of a body in any direction is called

as constraint Constraint is expressed as a force: reaction

Free Body Diagram(FBD)

Law of action and reaction Any pressure on a support causes an equal and opposite pressure

from the support so that action and reaction are two equal and opposite forces

Free body diagram(FBD) For a constrained body which is in equilibrium, the sketch in

which the body is isolated from its support and in which all forces acting on it are shown by vectors is called as a FBD Drawing a FBD is the first step of solving the engineering problem

Composition of several forces Successive application of the parallelogram law

Successive geometric addition(Polygon of forces)

Resolution of forces

When directions of both components are given Use parallelogram law

When both the direction and magnitude of one component are given Use triangle of forces