3. OUTLINES
INTRODUCTION
PLASTIC ANALYSIS WHY? WHAT?
STRESS STRAIN CURVE?
DIFFERENCE B/W ELASTIC AND PLASTIC ANALYSIS?
ASSUMPTIONS ?
PLASTIC HINGE?
PLASTIC MOMENT?
SHAFE FACTORS(RECTANGULAR,CIRCULAR,TRIANGULAR)
METHODS OF PLASTIC ANALYSIS
BASIC TERMINOLOGIES
DETERMINATION OF COLLAPSE LOAD
MECHANISM OF FAILURE
BEAM MECHANISMS
PROBLEM
4. INTRODUCTION OF PLASTIC ANALYSIS
In the method of plastic design of a structure, the ultimate
load rather than the yield stress is regarded as the design
criterion.
The term plastic has occurred due to the fact that the ultimate
load is found from the strength of steel in the plastic range.
This method is also known as method of load factor design
or ultimate load design.
5. Plastic Analysis - Why? What?
Behavior beyond elastic limit?
Plastic deformation - collapse load
Safe load – load factor
Design based on collapse (ultimate)
load – limit design
Economic - Optimum use of material
9. Elastic analysis
•Material is in the elastic
state
•Performance of structures
under service loads
•Deformation increases
with increasing load
Plastic analysis
•Material is in the plastic
state
•Performance of structures
under ultimate/collapse
loads
•Deformation/Curvature
increases without an
increase in load.
10. ASSUMPTIONS
Plane sections remain
plane in plastic
condition
Stress-strain relation is
identical both in
compression and
tension
Plane section remains
plane implying that the
strain distribution is
linear.
Deformation is small.
11.
12. Mechanical hinge Plastic hinge
Reality Concept
Resists
zero
moment
Resists a constant
moment MP
Mechanical Hinge Plastic Hinge with MP= 0
13. • M –Moment corresponding to working load
• My –Moment at which the section yields
• MP –Moment at which entire section is under yield stress
y
C
T
y
MP
14. Plastic moment
• Moment at which the entire section is
under yield stress
C T
Ac y Aty
2
c t A A
A
•NA divides cross-section into 2equal parts
2
yC T
A
15. y
y 2
yC
A
yt
c
AT
2 y
A
Similar to yZy
A
y y Z• Couple due to
2
y
2
y c t y p
Plastic modulus
Zp
1 is the shape factor
Z
16. Shape factor for various cross-sections
b
d
Rectangular cross-section:
Section modulus
bd 3
12I bd2
y d 2 6
Z
2
2 4
p c t
bd d d bd
Z
A
y y
2 4 4
Plastic modulus
Shape factor = 1.5
Zp
Z
Dept. of CE, GCE Kannur
16
Dr.RajeshKN
18
22. Methods of PlasticAnalysis
Static method or Equilibrium
method
• Lower bound:A load
computed on the basis of
an assumed equilibrium BM
diagram in which the
moments are not greater
than MP is always less than
(or at the worst equal to)
the true ultimate load.
Kinematic method or
Mechanism method
• Work performed by the external
loads is equated to the internal
work absorbed by plastic hinges
• Upper bound: A load computed
on the basis of an assumed
mechanism is always greater than
(or at the best equal to) the true
ultimate load.
25. MECHANISMS OF FAILURE
• A statically determinate beam will collapse if one plastic hinge is developed
• Consider a simply supported beam with constant cross section loaded with a point load P at
midspan
• If P is increased until a plastic hinge is developed at the point of maximum moment (just
underneath P) an unstable structure will be created.
• Any further increase in load will cause collapse
26. For a statically indeterminate
beam to collapse, more than
one plastic hinge should be
developed
The plastic hinge will act as
real hinge for further
increase of load (until
sufficient plastic hinges are
developed for collapse.)
As the load is increased,
there is a
redistribution of moment, as
the plastic hinge cannot
carry any additional
moment.
