Cantilever Beams

(1)

The Stress at the Support

(2)

If the cross section is Constant then this is the maximum stress

The Deflection is given by:-

(3)

The Maximum deflection is at the end and is:-

(4)

(5)

The Stress at the Support.

(6)

If the Cross-Section is Constant then this is the Maximum Stress.

The Deflection at any point is given by:-

(7)

The Maximum Deflection is at the end and is:-

(8)

(9)

Beyond the Load the stress is zero

At the Fixed End

(10)

If the Cross-section is Constant, then this is the Maximum Stress

The Deflection of any point between the Fixed end and the Load is :-

(11)

Beyond the load the Deflection is:-

(12)

The Maximum Deflection at the "Free" end is:-

(13)

Deflection at the Load:-

(14)

(15)

The Maximum Stress at the Fixed End

(16)

The Stesss is zero at . The greatest negative Stres is at and is:-

(17)

The deflection is given by:-

(18)

The maximum Deflection is at x = 0.5785 l and is:-

(19)

The Deflection at the centre is:-

(20)

The Deflection at the point of greatest negative Stress i.e.

(21)

(22)

Between the Support and the Load:-

(23)

Stress at the Fixed end. This is the maximum value

(24)

The Stress is Zero at

The Greatest negative Stress is at the centre and is

The Deflection of any Point between the Fixed End and the Load:-

(25)

The Deflection of any Point between the Support and the Load

(26)

The Maximum Deflection is at

(27)

The Deflection of the Load is:-

(28)

(32)

The Stress at the Support

(33)

The Stress at the Free End:-

(34)

These are the Maximum Stresses and are equal and opposite. The Stress is zero at the Centre.

The Deflection at any Point is:-

(35)

The Maximum Deflection is at the Free End and is:-

(36)