A simply supported wood beam with a span of L = 15 ft supports a uniformly distributed load of w0 = 270 lb/ft. The allowable bending stress of the wood is 1.95 ksi. If the aspect ratio of the solid rectangular wood beam is specified as h/b = 1.75, calculate the minimum width b that can be used for the beam.

The minimum width is

Explanation:

The free body diagram is shown on the first uploaded image

The Summation of the moment about A  is equal to 0 from the diagram we can see its wedged

     i.e

Given from the question that L = 15 ft

        =>

The net upward force experienced by the beam = 0

i.e             because of the canceling downward force

The maximum bending always occurs where the shear force is zero

To obtain the maximum bending moment

To obtain the width

The equation above is the bending equation

Where M is the bending moment  

Note: the multiplication by 12 is to convert the value to inches  

I is the moment of inertia

Note: the division by 12 is to convert the value to inches

and is the bending stress = 1.95 ×1000 ksi

Then y is the distance from natural axis =

Substituting this into the formula we have

  given that

                =>h = 1.75 b

     Substituting into the equation