## Analysis and Behavior of StructuresOffering students a presentation of classical structural analysis, this text emphasizes the limitations required in creating mathematical models for analysis, including these used in computer programs. Students are encouraged to use hand methods of analysis to develop a feel for the behaviour of structures. |

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Page 18

1 .4b and c, the normal

centroid of the cross section of z dFx about the y axis and y dFx about the z axis.

Summing (or integrating) these

...

1 .4b and c, the normal

**differential**force dFx creates moments with respect to thecentroid of the cross section of z dFx about the y axis and y dFx about the z axis.

Summing (or integrating) these

**differential**moments over the entire cross section...

Page 125

The user manual for the program must be consulted for the sign convention

before the program is used. 4.2

Transversely Loaded Beam The

transversely ...

The user manual for the program must be consulted for the sign convention

before the program is used. 4.2

**Differential**Equations of Equilibrium for aTransversely Loaded Beam The

**differential**equations of equilibrium for atransversely ...

Page 126

q(x) dx (1 q(x) * 7-Th Tve £ ^ Centroidal axis >M + dM V+dV\ 2 2 Centroidal axis -

(a) Beam segment under positive load (b)

centroidal axis Figure 4.2a-b Equilibrium considerations for beams. Simplifying ...

q(x) dx (1 q(x) * 7-Th Tve £ ^ Centroidal axis >M + dM V+dV\ 2 2 Centroidal axis -

(a) Beam segment under positive load (b)

**Differential**element of beam referred tocentroidal axis Figure 4.2a-b Equilibrium considerations for beams. Simplifying ...

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action analysis applied loads assumptions axial loads axis of symmetry behavior calculation centroidal chord column complementary virtual concentrated load conjugate beam constant cross section curvature diagram defined deformation system direct integration distributed load end moments equation of condition equations of equilibrium equilibrium equations Example Figure final moment diagram force in member forces and moments free body geometrically stable horizontal indeterminate influence line integration joint kips left end linear linear elastic loading diagram loads acting magnitude mathematical model maximum member forces ment method nonlinear materials numerical integration panel points portal frame positive reaction components rigid bodies rotation shown in Fig sign convention simply supported beam slope slope-deflection spreadsheet static determinacy statically determinate structures Step strains stress stress-strain relation struc structure of Fig summing moments superposition symmetric structure tion uniform load unit load unknown vertical deflection vertical displacement virtual force system virtual work principle zero