Important Answers: Transverse Loading on Beams and Stresses in Beam

TRANSVERSE LOADING ON BEAMS AND STRESSES IN BEAMS

1.     State the assumptions while deriving the general formula for shear stresses.

i. The material is homogenous, isotropic and elastic.

ii. The modulus of elasticity in tension and compression are same and the shear stress is constant along the beam width.

2.Define shear stress distribution.

The variation of shear stress along the depth of beam is called shear stress distribution.

3. Mention the different types of beams.

i. Cantilever beam,

ii. Simply supported beam,

iii. Fixed beam,

iv. Continous beam and

v. Over hanging beam

4. Write down the bending moment equation.

The bending equation M /I = σ/y =E/R

Where,

M –bending moment

I –moment of inertia of the section,

σ–bending stress at that section,

y –distance from the neutral axis,

E –Young’s   modulus   of   the   material,

R –radius of curvature of the beam.

5. What do you understand by the term point of contraflexure?

The point where the shear force changes its sign or zero is called as point of contraflexure.At this point the bending moment is maximum.

6. What is the value of bending moment corresponding to a point having a zero shear force?

The value of bending moment is maximum where the shear force changes it sign or zero.

7. Mention the types of supports.

 Roller support

Fixed support

Hinged or pinned support

8. Define bending moment in beam.

The bending moment of the beam may be defined as the algebraic sum of the moments of the forces,

to the right or left of the section.

9. Define shear force.

Shear force at any section is defined as the algebraic sum of all forces acting on either side of a

beam.

10. What is meant by Neutral axis of the beam?

It is an imaginary plane, which divides the section of the beam into the tension and compression zones on the opposite sides of the plane.

11. What is mean by compressive and tensile force?

The forces in the member will be compressive if the member pushes the joint to which it is connected whereas the force in the member will be tensile if the member pulls the joint to which it is connected.

12. How will you determine the forces in a member by method of joints?

In method of joint after determining the reactions at the supports, the equilibrium of every support is considered. This means the sum all vertical forces as well as the horizontal forces acting on a joint is equated to zero. The joint should be selected in such a way that at any time there are only two members, in which the forces are unknown.

13.  What are the benefits of method of sections compared with other methods?

1. This method is very quick

2. When the forces in few members of the truss are to be determined, then the method of section is mostly used.

14.   Define thin cylinder?

If the thickness of the wall of the cylinder vessel is less than 1/15 to 1/20 of its internal diameter, the cylinder vessel is known as thin cylinder.

15. What are types of stress in a thin cylindrical vessel subjected to internal pressure?

These stresses are tensile and are know as

  Circumferential stress (or hoop stress )

  Longitudinal stress

16. What is mean by circumferential stress (or hoop stress) and longitudinal stress?

The  stress  acting  along  the  circumference  of  the  cylinder  is  called circumferential  stress  (or

hoop stress) whereas the stress acting along the length of the cylinder is known as longitudinal stress.

17. What are the formula for finding circumferential stress and longitudinal stress?

Circumferential stress, f₁ = pd / 2t

longitudinal stress, f₂                   = pd / 4t

18. What are maximum shear stresses at any point in a cylinder?

Maximum shear stresses at any point in a cylinder, subjected to internal fluid pressure is given by (f₁ –f₂) / 2 = pd / 8t

19.  What are the formula for finding circumferential strain and longitudinal strain?

The circumferential strain (e₁) and longitudinal strain (e₂) are given by

19.   What are the formula for finding change in diameter, change in length and change volume of a cylindrical shell subjected to internal fluid pressure p?