In
physics forces can be described as push and pull which changes the object in
motion, In strength of material forces can be surface forces when distributed
over area of surface and body forces when distributed over volume of the body.
Surface
Forces - these are distributed over the area
of body e.g.- Pully
Body
Forces - these are distributed over the volume
of body e.g.-Shaft
Introduction to Strength of Material (SOM)-Mechanics of Deformable body
Strength of Material :-
It is study of internal resisting force developed due to elastic deformation of a body under the action of load.
Assumption made in Strength of Material Equation:-
Material is assumed to be homogeneous and isotropic.
Component is assumed to be prismatic.
Load is assumed as static load
Effect of self weight is neglected.
Static Load:-
When magnitude and direction is constant with respect to time.
Prismatic:-
All dimension are constant or same throughout the structure.
Homogeneous:-
Material is said it be isotropic, when it exhibit same elastic property at a point in a given direction.
Isotropic:-
Material is said it be isotropic, when it exhibit same elastic properties in any direction at a given point.
Wednesday 10 October 2018
Hi Every one welcome to my engineering blog.I am glad to introduce that we are starting new video series fully dedicated to FEA and CAE field . Manly we will cover some journal topics based on Hypermesh and Ansys Workbench software with theoretical concept.Hopeing that you will support the chnanel.
Pressure vessel is defined as closed
cylindrical or spherical container which is designed to hold or to store fluids at
pressure substantially different from ambient pressure.
Classification of Pressure Vessel.
1.based on d/t ratio:-
1.Pressure vessel whose d/t ratio is greater than 20 units, such type of vessel is categorized to Thin walled pressure vessel (d/t
≥ 20).
Ex. Boiler shell, LPG cylinder
pressure cooker, storage tank
2. Pressure vessel whose d/t ratio is less than 20 units, such type is called as Thick walled pressure
vessel (d/t≤20).
Ex. Hydraulic cylinder, gun Barrel,
Storage tank
under high pressure
2. Based on Shape
of shell
1. Cylindrical
pressure vessel
2.
Spherical pressure
vessel DO comment !!!!!! 1.Why Spherical vessel better then cylindrical pressure vessel? 2.Which vessel we should used for safety purpose? 3.Which vessel we should used, keeping manufacturing cost in mind?
Bursting of pressure vessel occurs circumferential.
Condition-1
At particular
pressure, when longitudinal stress in thin walled pressure vessel is greater than ultimate strength, circumferential bursting occurs in pressure vessel.
σL> sut
FF
=
FR
FF= (π D2 P)/4-------------------------------i
FR=σLxπ𝐷x𝑡--------------------------ii
(πD2P)/4 =σLxπ𝐷x𝑡
σL=σ2= σlongitudinal= pd/4t = σ1/2
Bursting of pressure vessel occurs longitudinally.
Condition-2
At particular pressure, when Hoops stress in thin walled pressure vessel is greater than ultimate strength, bursting occurs longitudinally in pressure vessel.
σh> sut
FF = 2xFR
FF= PxLxD-------------------------------i
FR=2xσhxLxt--------------------------ii
PxLxD= 2xσhxLxt
σh = σ1 = σhoop= pd/2t
Thin pressure vessel can be considered bi
axial state of stress
(due
to longitudinal
stress).
σ1 = σhoop = pd/2t
σ2 = σlongitudinal = pd/4t = σ1/2
In plane τmax
=(σ1-σ2)/2 = pd/8t
Absolute τmax
=σ1/2 = pd/4t
Strain
stress
Major principal strain
ε1=εhoop=δD/D----------i
ε1= 1/E [σ1-μσ2]-----ii
σ2 = pd/4t = σ1/2
Equating i & ii
εh=δD/D=σ1/2E x[2-μ]
εh =pd/4tEx[2-μ]
Minor principal
strain
ε2=εlongitudinal=δL/L----------i
ε2= 1/E [σ2-μσ1]-------------ii
σ2 = pd/4t = σ1/2
Equating i & ii
εL=δL/L=σ1/2E x[1-2μ]
εL= pd/4tEx[1-2μ]
Volumetric strain
δV/V=pd/4tEx[5-4μ]
Thickness
of the shell
Safe condition of design (σ max)ind ≤(σt )per
σ hoop ≤(σt )per
σ hoop cylindrical=pd/2t≤ (σt )per
σ hoop spherical=pd/4t≤ (σt )per
Thin
C.P.V
According to failure theory (MPST,MSST)
PD/2t= ≤(σt )per
t≥PD/2(σt)per+corrosion
Added
Thin
S.P.V
According to failure theory
(MPST,MSST,MDET)
PD/4t= ≤(σt )per
t ≥PD/4(σt)per+corrosion Added
Refer Static Structure Analysis for thin Pressure Vessel in Ansys for better understanding .
