### Deflection of Beams

• Calculate deflection using the equation of the elastic curve.

• Utilize the direct determination of the elastic curve.

• Derive the deflection and slope curves for a beam through integration of the moment-curvature relationship.

• Apply discontinuity functions and standardized solutions to simplify the calculation of deflection and slope curves for beams.

### Solved Example:

#### 47-2-01

Slope at a point in a beam is the:

### Solved Example:

#### 47-2-02

Which of the following is an elastic curve equation for shear force? (EI = flexural rigidity)

### Solved Example:

#### 47-2-03

Which of the following statements is/are true for a simply supported beam?

### Solved Example:

#### 47-2-04

Which of the following is a differential equation for deflection?

### Solved Example:

#### 47-2-05

The equation of deformation is derived to be $y = x^3 - xL$ for a beam as shown in the figure. Curvature of the beam at the mid-span (in units, in integer) will be: (GATE Civil 2021) Solution:

$y = x^2 - xL$ Curvature at the midsection is: $\dfrac{1}{R} = \dfrac{d^2y}{dx^2}$ $\dfrac{dy}{dx} = 2x - L$ $\dfrac{d^2y}{dx^2} = 2$