Force Method of Analysis: General Procedure

Brief procedure

Remove supports to make the structure statically determinate — the result is called theprimary structure or released structure.

1.

Calculate deflections at points where supports were removed.2.Determine (redundant) forces necessary to return supports to original position.3.

Detailed procedure

Determine number of redundant.1.Remove enough redundant to form a determinate, stable structure (this is the primary orreleased structure).

2.

Calculate displacements (y or θ) due to applied loads in primary structure where theredundant were removed.

3.

Calculate y or θ at same points due to the redundant in terms of the redundant (theunknowns).

4.

Sum y or θ at each redundant from applied loads and redundant and set equal to zero orknown displacement, in the case of a known support settlement. Solve equations for theunknown reactions, which may be a set of simultaneous equations.

5.

Use equilibrium equations to complete the analysis.6.

Suggested methods of computing deflections

Use table inside front cover if it fits. (or the IDE 110 superposition tables)1.Use moment-area or conjugate-beam method if there are concentrated loads only (M/EIdiagram with straight-lines).

2.

Use virtual work or Castigliano's second theorem if there are only distributed loads or bothconcentrated and distributed loads (M/EI diagram with curved lines).

3.

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1. release redundant support

2. compatibility of displacement

0 = -ΔB + Δ'BB

0 = -(downward displacement due to applied load) + (upwarddisplacement due to support reaction)

first subscript: point where deflection is specifiedsecond subscript: point where the unknown reaction acts

3. unit load at B acting in direction of BBy

Δ'BB = By fBB

f = linear flexibility coefficient = measure of deflection per unit load (m/N,ft/lb)

0 = -ΔB + By fBB

4. solve for By

5. solve for other reactions using equilibrium

EExxaammppllee 22:: 11sstt--ddeeggrreeee iinnddeetteerrmmiinnaattee

1. release redundant support

2. compatibility of rotation

0 = θA + θ'AA

0 = -(angle at A due to applied load) + (angle at A due to supportmoment)

first subscript: point where angle is specifiedsecond subscript: point where the unknown reaction acts

3. unit moment at A acting in direction of MMA

θ'BB = MA αAA

α = angular flexibility coefficient = measure of angular displacement perunit couple moment (rad/Nm, rad/lb-ft)

0 = θA + MA αAA

4. solve for MA

5. solve for other reactions using equilibrium

EExxaammppllee 33:: 22nndd--ddeeggrreeee iinnddeetteerrmmiinnaattee

fBB = deflection at B cause by unit load at BfBC = deflection at B cause by unit load at C

fCB = deflection at C cause by unit load at BfCC = deflection at C cause by unit load at C