## 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 126

q(x) dx (1 q(x) * 7-Th Tve £ ^

(a) Beam segment under positive load (b) Differential element of beam referred to

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 to

**centroidal**axis Figure 4.2a-b Equilibrium considerations for beams. Simplifying ...Page 194

Along some line in the x-y plane of the beam, which for linear materials is the

pure moment as is shown for the line A-B in Fig. 6.2c. Lines such as A,/?, above

the ...

Along some line in the x-y plane of the beam, which for linear materials is the

**centroidal**axis of the member, no deformation occurs due to the action of thepure moment as is shown for the line A-B in Fig. 6.2c. Lines such as A,/?, above

the ...

Page 196

For nonlinear materials the neutral axis will still coincide with the

when the cross section is symmetric with respect to both the y and z axes and if

the stress-strain relation itself is symmetric in tension and compression.

For nonlinear materials the neutral axis will still coincide with the

**centroidal**axiswhen the cross section is symmetric with respect to both the y and z axes and if

the stress-strain relation itself is symmetric in tension and compression.

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### Common terms and phrases

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