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.

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Concept:

Deflection and slope in a cantilever beam due to point load

Deflection at point (ΔB) = 

Slope at point B (θB) =  = 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) = 

The negative sign shows only the slope is anticlockwise.

Slope at A due to 10 kN point load (θ1) = 

Slope at A due to 20 kN point load (θ2) = 

Slope at A due to 20 kN point load (θ2) = 

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

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

Slope at A due to both loads (θA) = 

The slope at point A in a given beam is 

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