CIVL3310 STRUCTURAL ANALYSIS Professor CC Chang Chapter 7: Approximate Analysis of Statically...
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Transcript of CIVL3310 STRUCTURAL ANALYSIS Professor CC Chang Chapter 7: Approximate Analysis of Statically...
CIVL3310 STRUCTURAL ANALYSIS
Professor 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 kN
V=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?