A cantilever beam of span 3.5 m is subjected to two point loads as shown in the figure Calculate the slope at point A. Take EI as constant throughout the beam length.

Concept:

Deflection and slope in a cantilever beam due to point load

Deflection at point (ΔB) = \({PL^3\over 3EI}\)

Slope at point B (θB) = \(PL^2\over 2EI\) = slope at point C (θC)

Deflection at point (ΔC) = ΔB + θB × a

Note: The slope at point B and point C is the same, in the above case beam.

Calculation:

Given

Slope at A due to 10 kN point load (θ1) = \(-{10\times 3.5^2\over 2EI}\)

The negative sign shows only the slope is anticlockwise.

Slope at A due to 10 kN point load (θ1) = \(-{61.25\over EI}\)

Slope at A due to 20 kN point load (θ2) = \(-{20\times 1.5^2\over 2EI}\)

Slope at A due to 20 kN point load (θ2) = \(-{22.5\over EI}\)

Slope at A due to both loads (θA) = θ1 + θ2

Slope at A due to both loads (θA) = \(-{61.25\over EI}\) + \(-{22.5\over EI}\)

Slope at A due to both loads (θA) = \(-{83.75\over EI}\)

The slope at point A in a given beam is \(-{83.75\over EI}\)