Built in Beams II

The stress at any Point :-

(1)

The Maximum Stress is at the ends and is:-

(2)

The Stress is zero at

The Greatest negative Stress is at the centre and is

The Deflection at any Point is given by:-

(3)

The Maximum Deflection is at the Centre and is:-

(4)

The Stress between each end and the Load:-

(5)

The Stress at each end is :-

(6)

The Stress at the middle is:

(7)

These are the maximum Stresses and are equal and opposite. The stress is zero at

The Deflection at any point is given by:-

(8)

The Maximum Deflection is at the Load and is:-

The Stress at any Point within the segment of length a

(9)

The Stress at any point within the segment of length b

(10)

The Stress at the end next to segment of length a

(11)

The Stress at the end next to segment of length b

(12)

The Maximum Stress is at the end next to the shorter segment.

The Stress is Zero for:-

(13)

The Greatest negative stress is at the Load and is given by:-

(14)

The Deflection for the segment of length a is given by:-

(15)

The Deflection for the segment of length b is given by:-

(16)

The deflection at the Load is:-

(17)

Let b be the length of the longer segment and a the shorter one.

The Maximum Deflection is in the longer Segment and occurs at

(18)

The Stress at any Point is given by:-

(19)

The Maximum Stress is at Point A and is:-

(20)

The Stress is zero at

The greatest negative Stress is at and is:-

(21)

The Deflection at any Point is given by:-

(22)

The Maximum Deflection is at and is given by:-

(23)

The Deflection at the centre of each Span is:-

(24)

The Deflection at the point of greatest negative Stress is

(25)

Between The Stress is given by:-

(26)

(27)

Stress at the Support R is:-

(28)

The greatest Stress in the first span is at:-

(29)

And is

The greatest Stress in the second Span is at:-

(30)

And is

The Deflection between is given by:-

(31)

The Deflection between is given by:-

(32)

The above example is so complicated that convenient general expressions for the maximum deflections cannot be obtained

Between point A and the Load the Stress at any Point is:-

(33)

Between Point B and the Load the stress at any Point

(34)

The Maximum Stress at Point A

(35)

The Stress is Zero at:-

(36)

The greatest negative Stress is at the centre of the Span and is:-

(37)

Between Point A and the Load the Deflection at any point is:-

(38)

Between Point B and the Load the Deflection at any point is:-

(39)

The Maximum deflection is at

(40)

The Deflection at the Load is:-

(41)

Between the Stress is:-

(42)

Between the Stress is:-

(43)

Between the Stress is:-

(44)

Between the Stress is:-

(45)

Stress at the Load

(46)

(47)

Stress at Support R

(48)

Stress at load W_2

(49)

The greatest of these is the maximum Stress.

The Deflection between

(50)

The Deflection between

(51)

The Deflection between

(52)

The Deflection between

(53)

The Deflection at Load

(54)

The Deflection at Load

(55)