View Factor Orientation (or View factor or shape factor) plays an important role in radiation heat transfer. View factor is defined as, "fraction of radiation leaving surface 'i' and strike 'j' ". Summation Rule (View Factor) If there is are similar surfaces 'i' and 'j' , then: Blackbody Radiation Exchange Radiation Exchange between Opaque, Diffuse, Gray surfaces in an Enclosure 1. Opaque 2. Surfaces 3. Two surface enclosure Radiation Shield It is used to protect surfaces from radiation act like a reflective surface. References: Material from Class Lectures + Book named Fundamentals of Heat and Mass Transfer by Theodore L. Bergman + My knowledge. Photoshoped pics are developed. Some pics and GIF from Google. Videos from YouTube ( Engineering Sights ).
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Buckling
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Buckling:
Buckling (Discession of Stability of Structures) is defined as, "A deformation occurred due to compressive loads in vertical members".
Example: mainly columns, vertical members, etc.
Buckling is due to instability (change in configuration) NOT a failure through yielding.
The analysis and design of vertical prismatic members supporting axial compressive loads is carried out.
Failure of structures are presented by designing structures so that the maximum stresses and maximum displacements remain tolerable limits.
There are two primary concerns:
The strength of the structure i.e. its ability to support a load without experiencing excessive stresses.
The ability of the structure to support a specified load without undergoing unacceptable deformations.
Important Points:
Stability ↣ material's ability to support a given load without experiencing a sudden change in its configuration (or load carrying capability without no sudden change).
Failure ↣ is due to instability of structures (design), geometric failure.
If column buckles at load ↣ require supports.
Column collapse ↣ if stresses > critical load.
Buckling must be avoided in Structural design. For example: in earthquakes, building moves left and right which changes its configuration, so collapse.
Buckling Derivation:
Conditions of equilibrium are defined on the basis of above load equation
Ideal Columns With Pin Support:
Ideal columns are defined as, "one that is perfectly straight before loading and is made of homogeneous material".
Load is applied through the centroid of cross-section.
When critical load is reached, column will be on the verge of becoming unstable.
Critical Load is defined as, "the maximum axial load a column can support when it is on the verge of buckling".
Different Modes of Buckling is given by:
Critical load is independent of strength of material, depends on material stiffness.
Load carrying capability of column increases with moment of inertia.
Efficient column ↣ are those in which column's cross-section is located as far away as possible from centroidal axes (like hollow columns).
Columns will buckle about the principal axis of cross-section having least MOI.
Slenderness Ratio (L/r) ↣ is the measure of column's flexibility and help in classifying columns as short, long and intermediate.
Columns having slenderness ratio < minimum ratio ↣ are failed by yielding (not buckling) and are called Short Columns.
Critical Stress to Slenderness Ratio Diagram:
Columns not to fail by either yielding or buckling, its stress must remain underneath the curve.
It tells minimum slenderness ratio (which is the yielding point).
Euler Formula is not valid below min. slenderness ratio (yield value exceeded before buckling can occur).
Effective Length:
It represent the distance between zero-moment points is called Effective Length (Le). Many design codes provide column formula that use a dimensionless coefficient K is called Effective Length Factor.
Determine by Euler formula for critical load.
By using other supports.
Secant Formula:
Euler formula is derived assuming load applied through centroid and column are perfectly straight.
In reality columns are not always straight and generally load is applied eccentrically.
Now,
P/A to KL/r Curves:
Plot of ec/r^2 against stress and slenderness ratio (for A-36 steel i.e. structural steel).
If eccentricity increases, failure occur before it should be.
Graph shows big changes in load carrying capacity of a column with respect to e.
Column having high values of slenderness ratio fails at or near to Euler critical load.
Selection of 'e' is very important in column design.
References:
Material from Class Lectures + Book named Engineering Mechanics of Materials by R.C. Hibbeler (10th Edition) + my knowledge.
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