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Mechanical - Strength of Materials - Deflection of Beams

BEAMS DEFLECTION

**1.
List any four methods of determining slope and deflection of loaded beam?**

i)Double integration
method,

ii)Macaulay’s method,

iii)Moment area method
and

iv)Conjugate beam
method

**2.
What is the relation between slope, deflection and radius of curvature of a
beam?**

1/R =(d2y)/(dx2)

Where R =radius of curvature.

Y= deflection.

**3. State two assumptions made in theEuler’s
co **

i)The cross section of
the column is uniform throughout its length and

ii)The length of the
column is very long as compared to its cross sectional dimensions.

**4. State Slenderness ratio**

The ratio between
actual length to least radius of gyration Slenderness ratio = L / k

**5. Write the equivalent length of column for
a column.**

i)One end is fixed and other end is free Effective length
L= 2l

ii)Both ends are fixed Effective length L= l/2

**6. State
the limitations of
Euler’s formula. **

If the slenderness
ratio is small, the crippling stress will be high. But for the column material,
the crippling stress cannot be greater
than the crushing stress. In the limiting case, we can find the value of
slenderness ratio for which the crippling stress is equal to the crushing
stress.

**7. Describe the double integration method.**

While integrating twice the original differential equation,
we will get two constant C1 and C2. The value of these constants may be found
by using the end conditions.

**8. Calculate the effective length of a long
column, whose actual length is 4m when i)both ends are fixed ii)one end is
fixed while the other end is free?**

i)Both ends are fixed Effective length L= l/2 =4/2=2m

ii)One end is fixed while the other end is free Effective
length L= 2l=2x4=8m

**9. Define column**

A structural member which is subjected to axial
compressive load is known as column.

**10. Define crippling load**

The load at which the column just buckles is known
as crippling load.

**11. Define shear force and
bending moment?**

SF at any cross section is defined as
algebraic sum of the vertical forces acting either side of

beam.

BM at any
cross section is defined as algebraic sum of the moments of all the forces
which are placed either side from that point.

**12. When will bending
moment is maximum?**

BM will be maximum when shear force
change its sign.

**13. What
is maximum bending moment in a simply supported beam of span ‘L’subjected to
UDL of ‘w’over entire span?**

Max BM =wL^{2}/8

**14. In a simply supported
beam how will you locate point of maximum bending moment?**

The
bending moment is max. when SF is zero. Writing SF equation at that point and
equating to zero we can find out the distances ‘x’from one end .then find
maximum bending moment at that point by taking moment on right or left hand
side of beam.

**15. What is shear force
and bending moment diagram?**

It shows the variation of the shear
force and bending moment along the length of the beam.

**16.
****What are the types of
beams? **

1. Cantilever beam

2. Simply supported beam

3. Fixed beam

4. Continuous beam

5. over hanging beam

**17.
****What are the types of
loads? **

1. Concentrated load or point load

2. Uniform distributed load (udl)

3. Uniform varying load(uvl)

**18.
****Write the assumptions
in the theory of simple bending? **

1. The material of the beam is homogeneous and isotropic.

The beam
material is stressed within the elastic limit and thus obey hooke’slaw.

3. Each layer of the beam is free to
expand or contract independently about the layer, above or

below.

4. The value of E is the same in both compression and tension.

**19.
****Write the theory of
simple bending equation? **

Where,

M - Maximum bending moment I - Moment
of inertia

f - Maximum stress
induced

y- Distance from the neutral axis E -
Young’smodulus

R –Radius of neutral layer.

**20. Define: Neutral Axis**

The N.A
of any transverse section is defined as the line of intersection of the neutral
layer with the transverse section.

**21. Define: Moment of
resistance**

Due to
pure bending, the layers above the N.A are subjected to compressive stresses,
whereas the layers below the N.A are subjected to tensile stresses. Due to
these stresses, the forces will be acting on the layers. These forces will have
moment about the N.A. The total moment of these forces about the N.A for a
section is known as moment of resistance of the section.

**22. Define: Section
modulus**

Section
modulus is defined as the ratio of moment of inertia of a section about the N.A
to the distance of the outermost layer from the N.A.

Section
modulus,

Where, I –M.O.I about N.A

y_{max} - Distance of the
outermost layer from the N.A

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