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Module 1

Module 2

Module 3

Module 4

Deflection of Structures

Lecture 1

Lecture 2

Conjugate Beam Method

Lecture 3

Lecture 4

Lecture 5

Lecture 6

Lecture 7

Module 5

Module 6

Module 4 : Deflection of Structures

Lecture 2 : Conjugate Beam Method

Example 4.7 Determine the slope at A and deflection of B of the beam shown in Figure 4.9(a) using the conjugate beam

method.

Solution: The vertical reaction at A in the real beam is given by

The bending moment at any point X at a distance x from A is given by

The corresponding conjugate beam and loading acting on it are shown in Figure 4.9(b). The loading on the beam varies

parabolically with maximum value as .

The slope at A , in the original beam will be equal to the shear force at A in the conjugate beam, thus,

(clockwise direction)