3 differences in term of deflections and slopes for solid rectangle shape and I-section beam.?

Question

in a simple supported beam. solid rectangle beam and i beam.

Answer 1

The deflection of a simply supported beam is given by (5/384)*(wL^4)/EI

Where w is the distributed loading, l is the beam length, E is the youngs modulous a material property and I is the moment of inertia also known as the second moment of Area. (Slope has a similar equation but is dependent on L^3)

If both cross sections are made of the same material then the only variance in the two deflections is the moment of inertia I.

Because the I beam is designed to resist moment it has most of its mass in the flanges where it is furthest away from the centre of mass of the section and will therefore contribute most effectivly. Engineered materials often take advantage of this property of I beams to save materials, you can reduce the amount of material needed to satisfy strength and deflection requirements by using an I beam over a solid rectangle.


So for the same area an I beam will deflect less, resist more moment and be effecient where as a solid section will deflect more have a greater slope, resist less moment and be very inefficient

Answer 2

The I beam will have less deflection for the same given cross sectional area and length since its moment of inertia (If I recall the terminology correctly) is greater.

Answer 3

Number 12 brings back some memories for me. Uh huh. A star for you.