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 ? = = WI2/ 16EI

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

Deflection y = wl3 / 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 ? = wl3 / 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 = wl4 / 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 ? = wl2 / 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 = wl3 / 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 ? = wl3 / 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 = wl4 / 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.)

90o to the horizontal is known as column.

14.  Define column.

If the strut is vertical (i.e.) 90o 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.

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

It is the load to which the column is actually subjected to and is well below the 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 Le= Equivalent length of the column or strut.