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MECHANICS - CASE STUDY SOLUTION


Aquarium Viewing Tank Wall

 

A new aquarium plans a large fish tank with a water depth of 3 meters. One of the walls will be constructed from Plexiglas and supported by vertical I-beams. The beams will be spaced every 2 meters. The water pressure will cause a distributed load on the beams. The beams can be modeled as a cantilever beams since the base is fixed and the top end is free. The minimum weight S type I-beam needs to be specified using the beams listed in the appendix.

   
  Loading


Distributed Load on Beam

 

The water will cause a pressure on the wall which is a linear function of the depth. The pressure on the wall will be

     p = h g ρ

where ρ is the water density and g is the gravitational constant, 9.81 m/s2. The maximum pressure will be at the bottom, h = 3 m,

     p = (3 m) (9.81 m/s2) (1 g/cm3)

        = (3 m) (9.81 kN/m3) = 29.43 kN/m2

The pressure now needs to be converted to a distributed load on a typical vertical beam. There is one beam for every 2 meters, so the maximum distributed load at the bottom is

     wmax = (29.43 kN/m2 )(2 m) = 58.86 kN/m

     
    Moment


Free Body Diagram of Beam

 

The maximum moment for a cantilever beam is at the base. The distributed load has an equivalent load of

     F = 0.5 (58.86 kN/m)(3 m ) = 88.29 kN

Summing moments at the base gives,

     ΣMbase = 0

     Mmax - (88.29 kN)(1 m) = 0

     Mmax = 88.29 kN-m

   
    Section Modulus

   

Now that the moment is known and the yield stress is given, the section modulus can be determined. There is a factor of safety of 3.0 that will reduce the allowable stress.

     Srequired = M/σ = 88.29 kN-m / (250,000/3 kN/m2 )

        = 1,059 × 103 mm3

Looking at the appendix listing of all S type I-beams (note, SI units) give the lightest beam with at least 1,059 × 103 mm3 as

     S380 x 74

This beam type has a section modulus of 1,060 × 103 mm3 so it will just barely work.

     
   
 
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