Advanced Methods of Structural Analysis

8.3 Comparison of the Force and Displacement Methods 291

8.3 Comparison of the Force and Displacement Methods................

The force and displacement methods are theprincipal analytical methods in struc-
tural analysis. Both of these methods are widely used, not only for static analysis,
but also for stability and dynamical analysis. Below we will provide a comparison
pertinent to the two methods’ presentation in their canonical forms.
Both methods require construction of primary systems. Both methods require
construction of bending moment diagrams for unit exposures (forces or displace-
ments). In both methods, a difference between the primary system and the original
one is eliminated using the set of canonical equations.
Fundamental differences between these methods are presented in Table8.4.It
can be easily seen that these methods are duel, i.e., one column of the table can be
obtained from the other by linguistic restatement.

Ta b l e 8. 4 Fundamental differences between the force and displacement methods
Comparison criteria Force method Displacement method

Primary system
(PS)

Obtained byeliminating

redundantconstraintsfroma

structure

Obtained byintroducing

additionalconstraintstoa

structure

Primary
unknowns
(PU)

Usesforces(forces and moments),

whichsimulatethe actions of

eliminatedconstraints

Usesdisplacements(linear and

angular), whichneutralizethe

actions ofintroduced

constraints

Reactions of eliminated

constrains are PU

Displacements of induced

constraints are PU

Number of PU Equals the degree ofstatical
indeterminacy

Equals the degree ofkinematical

indeterminacy

Number of PS
and way of
obtaining PS

Nonunique.PScan be chosenso

that all redundant constraints

must be eliminated and

replaced by corresponding

reactions (forces and/or

moments)

Which redundant constraints

should be eliminated is a matter

of choice, but the obtained PS

should be statically determinate

Unique.PSmust be constructed

so that in every rigid joint an

additional constraint is

introduced to prevent angular

rotation; and for every

independent linear

displacement an additional

constraint is introduced to

prevent linear displacement

PS presents a set of standard

statically indeterminate beams

Canonical
equations

ı 11 X 1 Cı 12 X 2 CC1PD 0

ı 21 X 1 Cı 22 X 2 CC2PD 0



r 11 Z 1 Cr 12 Z 2 CCR1PD 0

r 21 Z 1 Cr 22 Z 2 CCR2PD 0



Number of canonical equations

equals the number of PU

Number of canonical equations

equals the number of PU

(continued)