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Civil - Mechanics Of Solids - Deflection Of Beams

BEAMS DEFLECTION

**1. What
are the different methods used to find out the slope and deflection at a
section in a loaded Beam?**

(i) Double integration
method(ii) Moment area method(iii) Macaulay's method

**2. Define
Mohr's theorem I **

It states that the change
of slope between any two points, on an elastic curve, is equal to the net area
of B.M. diagram between these points divided by EI.

*Slope ? = A/EI*

*3.
Derive double integration method.*

*M
= Moment resistance of a beam at a point P x and y be the co-ordinates of point
P, then*

*4. **Define Mohr's theorem II*

*It states the
intercept taken on a vertical reference line of tangents drawn at any two
points on an elastic curve is equal to the moment of the bending moment diagram
between these points about the reference line divided by EI.*

*What will be the max slope of elastic curve for a simply supported beam
length (l) subjected to a downward concentrated load W act at center?*

*Slope ? = = WI ^{2}/ 16EI*

*6.
**What
will be the maximum deflection of elastic curve for a simply supported beam
length **(l) subjected to
a downward concentrated load W act at center? *

*Deflection y =* wl^{3} /
48EI

*7.
**What
will be the max slope of elastic curve for a simply supported beam length (l)
subjected to a uniformly distributed load w/m over the entire span? *

*Slope ? =*
wl^{3} / 24EI

*8.
**What
will be the maximum deflection of elastic curve for a simply supported beam
length (l) subjected to a uniformly distributed load w/m over the entire span? *

*Deflection y =* wl^{4} /
384EI

*9.
**What
will be the max slope of elastic curve for a cantilever beam length (l)
subjected to a point load w act at the free end? *

*
Slope ? =* wl^{2} /
2EI

*10. What will be
the maximum deflection of elastic curve for a cantilever beam length (l)
subjected to a point load w act at the free end?*

*Deflection y =* wl^{3} /
3EI

*11. What will be
the maximum deflection and max slope of elastic curve for a cantilever beam
length (l) subjected to a u.d.l w N/m act over the entire span?*

*Slope ? =*
wl^{3} / 6EI

*12. What will be
the maximum deflection of elastic curve for a cantilever beam length (l)
subjected to a u.d.l w N/m act over the entire span?*

*Deflection y =* wl^{4} /
8EI

*13.
Define strut.*

*A
member of structure or bar which carries an axial compressive load is called
the strut. If the strut is vertical (i.e.)*

*90 ^{o}
to the horizontal is known as column.*

*14.
Define column.*

*If
the strut is vertical (i.e.) 90 ^{o} to the horizontal is known as
column.*

*15. Define Slenderness ratio.*

*It is the ratio
of unsupported length of the column to the minimum radius of gyration of the
cross sectional ends of the column.*

*16. Define buckling factor.*

*It
is the ratio between the equivalent length of the column to minimum radius of
the gyration.*

*17. Define buckling load.*

*The maximum
limiting load at which the column tends to have lateral displacement or tends
to buckle is called the buckling or crippling load.*

*18. Define safe load.*

*It
is the load to which the column is actually subjected to and is well below the
buckling load.*

*Safe
load= buckling load.*

*Factor of safety*

*19. Define short column.*

*Columns which
have lengths less than 8 times their respective diameters or slenderness ratio
less than 32 are called short columns*

*20. Define medium size column.*

*Columns which
have lengths varying from 8 times to 30 times their respective diameters or
slenderness ratio lying between 32 and 120 are called medium size columns.*

*21. Define equivalent length.*

*The
distance between adjacent points of inflexion is called equivalent length or
effective length.*

*22. What is the formula for calculating the
critical load for a column or strut?*

*P= critical load E= youngs modulus*

*I = Least moment of inertia of the section of
the column L _{e=} Equivalent length of the column or strut.*

*23. What is Rankines formula for **calculating Rankine's load.*

*s*_{c}* -Max. possible compressive stress*

*A- cross
sectional area, a- **Rankine's
constant.*

*L _{e} *

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