Question

W300x0.51 steel section is used in a 3 m cantilever span. Compute the maximum deflection due to concentrated load of 267 kN at the midspan. If the allowable deflection is 1/360 of the span check whether the beam meets the deflection requirements or not

Answer 1

Solution:-

Cantilever beam length (L) = 3 m

Point Load (P) = 267 kN

Steel Section = W300X0.51 ,

Elastic modulus of steel =  

From AISC steel section properties manual ,

W300X0.51 Properties is

Moment of inertia about X-X axis

Moment of inertia about Y-Y axis

So that maximum moment of inertia is

BY MOMENT AREA METHOD,

Deflection at Midspan of cantilever beam is given by as,

------------------------Eq.A

Where,

A = Area of bending moment diagram

= Distance of C.G. of area of B.M. diagram from Free end

Let's First determine maximum bending moment in beam is

P = Load = 267 kN

x = span length

Then,

Bending moment at fixed end A is

From Eq.A

Deflection at Midspan Point C is

Where,

= Distance of C.G. of area of B.M. diagram from Free end

Put all data in equation A.

   (All unit converting meter to milimeter)

Deflection Check:-

As per question given

Maximum deflection is limited ti 1/360 of the span.

So that Maximum deflection is

So that maximum deflection is grater then actual deflection.

Hence,

  Ans.

So that beam is safe in deflection criteria.