Struct2 Lecture Notes #2 (Truss Analysis & Deflection).pdf

Notes in Structural Analysis II – Glenn M. Pintor / De La Salle University

Truss Analysis, Elastic Strain Energy

Truss

! Structure composed of slender members joined together at their ends

! Design assumptions:

o Members are joined by smooth pins (even for welded or bolted connections):

" Ensure centrelines of joining members are concurrent at a point

" Considering the effects of having rigid connections, neglect secondary stresses

due to expected bending of member associated with internal loadings

o All loading are applied at the joints

Common types of Trusses

! Scissors – for short spans requiring overhead clearance

! Howe & Pratt – for moderate span of 18~30 meters

! Fan or Fink – for larger spans, may be built with cambered bottom chord

! Sawtooth – used where column spacing is acceptable, uniform lighting is required

! Bowstring – used for garages, airplane hangars

! Arch – for field houses, gymnasiums

Bridge truss components

! Deck

! Stringers

! Floor beams

! Bracing elements: lateral, sway, portal



Classification of Simple Trusses

! Simple – simplest rigid and stable framework: triangle

! Compound – formed by connecting several simple trusses

! Complex



Criterion for Determinacy

! Typical truss analysis problems involve determination of the following:

o Internal forces in b number of truss members

o External support reactions r

! Check for determinacy: assumes rotational equilibrium is automatically satisfied at the joints,

only requires to satisfy translational / force equilibrium at the joints



Stability



Truss Analysis

! METHOD OF JOINTS





EXERCISES





! METHOD OF SECTIONS





Elastic Strain Energy

! For calculation of displacements & slopes for trusses and frames (and complicated loadings in

beams), use energy methods

! Application of conservation of energy principle: work done by external forces is transformed

into internal work (or strain energy) which is developed when structure deforms

Ue = Ui or

! External work of force:

! External work of moment:

! Strain energy - axial force:

! Strain energy – bending moment:



Virtual Work Method

1. Apply a “virtual” unit load P’=1 that acts in the same direction as !. This cause internal

loading u

2. Apply the real loading P1, P2, … , Pn. Suppose these cause displacement and internal

deformation dL.

where

P’ = 1 = external virtual unit load acting in the direction of !

u = internal virtual load acting on the element in the direction of dL

! = external displacement caused by the real loads

dL = internal deformation of the element caused by the real loads

Method of Virtual Work: Trusses

Procedure for analysis – External Loading:

1. Apply virtual load P’=1 on the structure in the direction of required deflection

2. Calculate the internal load, ie, axial forces n in each member due to the virtual load

3. Calculate the internal load, ie. Axial forces N in each member due to the read load.

4. Apply the equation of virtual work:

5. If the resultant sum is positive, the displacement ! is in the same direction as the

unit load. Otherwise, ! is opposite to the unit load.

Struct2 Lecture Notes #2 (Truss Analysis & Deflection).pdf

Documents

structural analysis

elastic strain energy

strain energy bending

energy principle

strain energy axial

energy methods

portal notes

complex notes