01 intro to statics

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1 Introduction to Statics andStructural Analysis

K L 2 1 0 3 , C L A S S 0 2

S E M E S T E R I 2 0 1 2 / 2 0 1 3

Definitions

Mechanics: the physical science which deals with.

Statics: part of mechanics which concerns theequilibrium of bodies under action of forces.

Dynamics: part of mechanics which concerns themotion of bodies under action of forces.

support loads (in more general term: “body”).



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Structural Analysis

The process to determine how a structure responds tos ecified loads based on the a lication of h sicallaws (engineering mechanics) and mathematics.

Primary objective:computation of reactions,internal forces, stresses,

.

Fundamental relations:equilibrium, constitutive,and compatibility.

Scalars and Vectors

Scalar quantities: only associated with magnitude.

magnitude. Free vector: not confined to a unique point or line in space.

Sliding vector: has a line of action but not at a unique point ofapplication. The vector can be applied at any point along theline of action. Example: When an external force acts on a body, the force can be

external effect on the body. (see principle of transmissibility inChapter 2)

Fixed vector: has a unique point of application

Example: In calculations of internal forces due to an applied force,the force must be treated as a fixed vector.



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Vector Addition

Parallelogram rule

Triangle rule

Vector subtraction

Component of a Vector

Two vectors (or three for vector in space) whose sum

vector.

Components of a vector are related to vector addition. Use parallelogram ruleto determine the components of a vector.

Components of a vector are not always equal to the projections of the vectoronto the same axes. They will be the same only if the axes are perpendicular toeach other (figures (b) and (c) above).



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Units

Unit SI US

length meter (m)foot (ft., ’ )

inch (in., ” )

time second (s) second (s)

force Newton (N) pound (lb)

1 N = 1 kg-m/s2

1 slu = 1 lb-s2 ft

g = 9.81 m/s2 = 32.2 ft/s2 = 386.4 in/s2

Accuracy and Approximations

Accuracy to three significant figures is considered.

However, keep all the digits in the calculation toavoid round-off errors.

Small-angle approximations are commonly used instructural analysis (fairly accurate up to 0.2 radianor about 10o):

sin θ ≈ θ ; tan θ ≈ θ ; cos θ ≈ 1



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Problem Solving

Formulate the problem .

State the desired result(s).

State your assumptions (if any).

Develop the solution

Draw any diagrams you need to understand the relationships.

State the governing principles/equations.

Make your calculations. Check the consistency of the units.

Ensure that the answers are reasonable in terms of magnitude,directions, common sense, etc.

01 intro to statics

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