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Thursday, January 17, 2019
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Saturday, January 12, 2019
Example of Influence line diagram (Truss)
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Influence line diagram(Truss)-Theory
Influence Line Diagram(Beam ) -
1. Standard method
2. Muller Breslau Method
Influence-Line -diagram-(Truss)
Influence Line diagram (ILD) for Truss members
ILD represents how Axial force changes overtime in each
members of truss when unit load moves from one side to another i.e. Effect of unit moving load on member if truss.
Q. How do we draw ILD for truss member ?
Note : Since we are dealing with moving load so we need to
determine path of travel for load.
Here in this both figure Red marking members are the path of travel .
Concept involved in drawing ILD in truss :
To draw the ILD for specific member we find the axial force in the member every time the unit load visit the joint .
Here , in above figure Orange Dot shows the joints which Unit load visits.
Thus to draw ILD for particular member , we need to do calculation for that member by placing unit load on each of the joints which the unit load visit .
Note : When unit load is just above the supports Axial Force at every member is Zero.
To understand on detail we will solve few Examples :
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Influence Line Diagram for beams Standard and Muller Breslau Method
Influence-Line-Diagram-(Standard-Method)
Here we discussed about Standard method for Drawing Influence Line Diagram . There is lot easy method to draw ILD which we use in solving MCQs and Solution i.e. Muller Breslau Method . To learn Click Here.
Friday, January 11, 2019
MOhr's Circle
Mohr's Circle
• It is termed as the graphical form where transformation equations of plane stress can be signified.
• This representation is very useful since it allows you to imagine the normal and shear stress relationships acting on different inclined planes at a point in a stressed body.
• This circle is useful for the computation of principal stresses, stresses on inclined planes, and maximum shear stresses.
• This method is easy and clear approach.
Equation:
Stress transformation equations:
Here, σx1 is the stress on x1 surface, σx ,σy are the stress on x, y surface, τ xy is shear stress on x, y surface, θ is the angle, τ x1y1 is the shear stress on x1y1 surface.
Show the principal stress diagram as in Figure (1).
Show the inclined position principal stress diagram as in Figure (2).
Procedure:
• Draw a couple of coordinate axes with σx1 as positive to right and τx1y1 as positive downward.
• Place point A, indicating conditions of stress on element x face by plotting its coordinates σx1= σx and τ x1y1= τxy . A point on circle corresponds to q = 0 °.
• Situate point B, it represents stress conditions on element y face by plotting its coordinates σx1= σy and τx1y1= − τxy. B point on circle corresponds to q = 90 °.
• Plot a line from point A to B, a circle diameter passing through point c. A and B points are at diameter opposite ends.
• Draw Mohr’s circle through points A and B using circle center c. This circle radius is R and center c having coordinates of σx1=σavg and τ x1y1= 0.
Show the Mohr circle diagram as in Figure (3).
Applications:
• This technique is used in analysis of finite homogeneous strain and moment of inertia determination.
• The main benefit of this circle is that principal stresses and maximum shear stress are obtained instantly after plotting the circle.
• Values of obtained principal stress data is utilized in material failure theories to predict.
Properties of Materials
Properties of materials
1. Elasticity :
When a material is loaded
with elastic limit and which on being unloaded at elastic limit regains its
original shape, this property of material is known as elasticity. The material
showing the elastic property up to certain limit is known as elastic limit, is
called elastic material. If the material is stressed beyond this limit full
recovery is not possible, some permanent deformation will be left unrecovered.
This part is irrecoverable is called Permanent
Set.
2. Creep
:
If we apply same load for
long duration of time, without increasing the load, deformation increases. Thus
creep is the property of a material by virtue of which a material continues to
deform with time under sustained or constant loading.
3. Brittleness
:
The tendency to break
under an impact of load is called brittleness. It is opposite to ductility.
4. Ductility :
It is the property of
being permanently extended by tensile force to smaller section before it
fracture. Commonly it is a property of material to be wire .
5. Endurance
Limit :
The stress below which a
material has a probability of not failing under reversal stress is known as
Endurance limit.
6. Fatigue
:
The phenomenon of
decreased resistance of a material due to dynamic loading i.e reversal of
stress is known as fatigue.
7. Hardness
:
It is the property which
offer resistance to abrasion ( ability of material which resist against being
scratched ). It is expressed in terms of Moh’s scale.
8. Malleability
:
It is the property of
being permanently extended into sheets without fracture when rolled or
hammered.
9. Plasticity
:
It is opposite property of
elasticity . A perfectly pastic material is material which doesn’t return to
its original shape when the loading causing deformation is removed.
10. Resilience
:
The strain energy stored
in a material when strained within the elastic limit , is known as resilience and maximum energy stored in
material at elastic limit is known as
proof resilience.
11. Stiffness
:
It is that property of
material due to which material can resist deformation.
12. Tenancy
:
Ultimate tensile strength
of material is called tenancy.
13. Toughness:
It is the property of
material which enables it to absorb energy at high stress without fracture. The
resistance if material to fracture by bending, twisting, fatigue, or impact of
load is known as toughness.
Stress-Strain Curve
Stress-strain
graph:
It's a graph which represents stress value
against strain value of the given material,when the material is subjected to
increasing pull. It is the characteristics properties of the Materials.
1.
proportional limit: it is
the point upto which hookes law is applicable ie., stress is directly
proportional to strain i.e. Portion OA. Stress and Strain are linearly
proportional.
2.
Elastic limit: there is always the limiting value of load up to which strain
totally disappears on removal of load i.e. Point B. If we unload on point B , unloading curve will be
B-A-O i.e. no permanent deformation
happens but Stress is not linearly proportional to strain.
a.
material
posses elastic nature and properties till elastic limit.
b. upto this point material obtains its original
configuration on removing load.
3.
Yield point: The
stress beyond which material becomes plastic.
Point “C”
Upper yield point i.e. Load just before yielding starts.
Pont “ D”
Lower yield point i.e. Actual point where yielding will take place.
# For
practical purpose we take C and D as same.
# yield point for particular material is defined
with Point “D”.
4.
Ducticle point: beyond
this point neck forms where the local cross sectional area becomes significantly
smaller than original. Point D onwards till point E . Rate of strain is very
high i.e. strain is increases at rapid rate as compared to stress.
a. material
acquires plastic nature .
5.
Ultimate point: The
point at upto which material can withstand maximum load and ultimate strength
with maximum elongation i.e. Point E .
Strain hardening of material occurs due to the change in crystalline structure
of material.
a. large
deformation possible before failure.
6.
Point of rupture: the
stress which makes the material failure or break. Zone EF. After point E cross-section
of the specimen starts to reduce known
as necking.
Wednesday, January 9, 2019
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