### 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
[email protected]/* <![CDATA[ */!function(t,e,r,n,c,a,p){try{t=document.currentScript||function(){for(t=document.getElementsByTagName('script'),e=t.length;e--;)if(t[e].getAttribute('data-cfhash'))return t[e]}();if(t&&(c=t.previousSibling)){p=t.parentNode;if(a=c.getAttribute('data-cfemail')){for(e='',r='0x'+a.substr(0,2)|0,n=2;a.length-n;n+=2)e+='%'+('0'+('0x'+a.substr(n,2)^r).toString(16)).slice(-2);p.replaceChild(document.createTextNode(decodeURIComponent(e)),c)}p.removeChild(t)}}catch(u){}}()/* ]]> */ 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
Example 7.3
Determine (approximately) the moment at the joints
E and C.
Inflection
point
1 degree
indeterminacy
hinge
Example 7.4
Determine (approximately) the forces acting in the
members of the Warren portal.
• Portal method
Inflection points
Shear forces
• Cantilever method
Inflection points
Axial forces
7. Approximate Analysis
• Structural analogy
• What are inflection points?
• How to analyze frames under vertical