Transcript Ch 7

Chapter 7:
Approximate Analysis of Statically Indeterminate Structures
CIVL3310 STRUCTURAL ANALYSIS
Professor CC Chang
Approximate Analysis


Preliminary analysis for complex indeterminate
structures
Involve some assumptions & different answers are
possible
Structural Analogy
12 m
C=T=67.5 kN
20 kN 20 kN 20 kN 20 kN 20 kN
6@9 m= 54 m
M=810 kN∙m
V=30 kN
12 m
20 kN 20 kN 20 kN 20 kN 20 kN
Fy=30 kN
F cos   shear  10
50 kN
50 kN
Shear
(kN)
moment
(kN∙m)
FBK=37.5 kN
Structural Analogy
3 degrees of indeterminacy
P1
P2
R1
Stiff diagonal members
assume Fa=Fb
Weak diagonal members
assume Fb=0 (no compression)
R2
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 Points
Points of zero moment: internal hinges
(Deflection shape: zero curvature)
Inflection Points
Clamped BC
Under UDL
Inflection Points
Assumed clamped
Location: 0.2L
Inflection Points
0.2L
0.2L
L
Frames under Vertical Loads
Frames under Vertical Loads
Example 7.3
Determine (approximately) the moment at the joints
E and C.
Frames under Horizontal Loads
Inflection
point
1 degree
indeterminacy
hinge
Frames under Horizontal Loads
Frames under Horizontal Loads
Example 7.4
Determine (approximately) the forces acting in the
members of the Warren portal.
Frames under Horizontal Loads
• Portal method
Inflection points
Shear forces
Frames under Horizontal Loads
• Cantilever method
Inflection points
Axial 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?