UNIT –IV
DEFLECTION OF BEAMS AND SHEAR STRESSES
1. What are the methods for finding out the slope and deflection at a section?
The important methods used for finding out the slope and deflection at a section
in a loaded beam are
1. Double integration method
2. Moment area method
3. Macaulay’s method
The first two methods are suitable for a single load, where as the last one is
suitable for several loads.
2. Why moment area method is more useful, when compared with double
integration?
Moment area method is more useful, as compared with double integration method
because many problems which do not have a simple mathematical solution can be
simplified by the ending moment area method.
3. Explain the Theorem for conjugate beam method?
Theorem I : “The slope at any section of a loaded beam, relative to the original
axis of the beam is equal to the shear in the conjugate beam at the corresponding section”
Theorem II: “The deflection at any given section of a loaded beam, relative to the
original position is equal to the Bending moment at the corresponding section of the
conjugate beam”
4. Define method of Singularity functions?
In Macaulay’s method a single equation is formed for all loading on a beam, the
equation is constructed in such away that the constant of Integration apply to all portions
of the beam. This method is also called method of singularity functions.
5. What are the points to be worth for conjugate beam method?
1. This method can be directly used for simply supported Beam
2. In this method for cantilevers and fixed beams, artificial constraints need
to be supplied to the conjugate beam so that it is supported in a manner
consistent with the constraints of the real beam.
6. What are the different sections in which the shear stress distribution is to be
obtained?
• Rectangular section
• Circular section
• I- section
• T- section
• Miscellaneous section
7. What do you mean by shear stress in beams?
The stress produced in a beam, which is subjected to shear forces is know as
stresses.
8. What is the formula to find a shear stress at a fiber in a section of a beam?
The shear stress at a fiber in a section of a beam is given by
_
F x AY
q = _______
I x b
F = shear force acting at a section
A = Area of the section above the fiber
--
Y = Distance of C G of the Area A from Neutral axis
I = Moment of Inertia of whole section about N A
b = Actual width at the fiber
9. What is the shear stress distribution rectangular section?
The shear stress distribution rectangular section is parabolic and is given by
q = F/2I [d2 /4 – y2]
d = Depth of the beam
y = Distance of the fiber from NA
10. What is the shear stress distribution Circular section?
q = F/3I [R2-y2]
11. State the main assumptions while deriving the general formula for shear stresses
The material is homogeneous, isotropic and elastic
The modulus of elasticity in tension and compression are same.
The shear stress is constant along the beam width
The presence of shear stress does not affect the distribution of bending stress.
12. Define: Shear stress distribution
The variation of shear stress along the depth of the beam is called shear stress
distribution
13. What is the ratio of maximum shear stress to the average shear stress for the
rectangular section?
Qmax is 1.5 times the Qavg.
14. What is the ratio of maximum shear stress to the average shear stress in the case
of solid circular section?
Qmax is 4/3 times the Qave.
15. What is the shear stress distribution value of Flange portion of the I-section?
q= f/2I * (D2/4 - y)
D-depth
y- Distance from neutral axis
16. What is the value of maximum of minimum shear stress in a rectangular cross
section?
Qmax=3/2 * F/ (bd)
17. What is the shear stress distribution for I-section?
The shear stress distribution I-section is parabolic, but at the junction of web and
flange, the shear stress changes abruptly. It changes from F/8I [D2 –d2] to B/b x F/8I [D2
–d2] where D = over all depth of the section
d = Depth of the web
b = Thickness of web
B = Over all width of the section.
18. How will you obtained shear stress distribution for unsymmetrical section?
The shear stress distribution for Unsymmetrical sections is obtained after
calculating the position of N A.
19 Where the shear stress is max for Triangular section?
In the case of triangular section, the shear stress is not max at N A. The shear
stress is max at a height of h/2
20. Where shear stress distribution diagram draw for composite section?
The shear stress distribution diagram for a composite section, should be drawn by
calculating the shear stress at important points.
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