CIVL3310 STRUCTURAL ANALYSISProfessor CC Chang

Chapter 7: Approximate Analysis of Statically Indeterminate

Structures

Approximate Analysis Preliminary analysis for complex

indeterminate structures Involve some assumptions & different

answers are possible

Structural Analogy

20 kN 20 kN 20 kN 20 kN 20 kN

20 kN 20 kN 20 kN 20 kN 20 kN

12 m

6@9 m= 54 m

50 kN 50 kN

Shear(kN)

moment(kN∙m)

12 m

M=810 kN∙m

C=T=67.5 kNV=30 kN

Fy=30 kN

FBK=37.5 kN10shearF cos

Structural Analogy3 degrees of indeterminacy

P1 P2

R1 R2

Stiff diagonal membersassume Fa=Fb

Weak diagonal members assume Fb=0 (no compression)

Example 7.1• Determine (approximately) the forces in the members

of the truss. The diagonals are designed to support both tensile and compressive forces

Inflection PointsPoints of zero moment: internal hinges

(Deflection shape: zero curvature)

Inflection Points

Clamped BCUnder UDL

Inflection Points

Assumed clampedLocation: 0.2L

Inflection Points

L

0.2L 0.2L

Frames under Vertical Loads

Frames under Vertical Loads

Example 7.3Determine (approximately) the moment at the joints E and C.

Frames under Horizontal Loads

hinge

1 degree indeterminacy

Inflectionpoint

Frames under Horizontal Loads

Frames under Horizontal Loads

Example 7.4Determine (approximately) the forces acting in the members of the Warren portal.

Frames under Horizontal Loads• Portal method

Inflection pointsShear forces

Frames under Horizontal Loads• Cantilever method

Inflection pointsAxial forces

7. Approximate Analysis• Structural analogy• What are inflection points?• How to analyze frames under vertical

loads?• How can inflection points be used to

simplify the analysis?• What are portal method and

cantilever method?