Thursday, March 23, 2017

Simply supported or fixed end?

Simply supported or fixed end? This might seem a small decision to make but the engineer's preference on this matter has a major impact in design, economy and appearance of the structure. When to design a beam as simply supported and when to design as fixed end? May this discussion be helpful to my fellow structural designers.


A. Properties of a simply supported beam
  1. There is no bending moment at the supports.
  2. The maximum bending moment is somewhere at the middle of the beam depending on type of loading. 

B. Properties of a beam with both ends fixed
  1. There is bending moment at the supports and at the middle.
  2. The maximum bending moment is at the supports. 
C. Comparison between simply supported and fixed end 
  1. Both has the same shear at support.
  2. Assuming they are to carry the same load, the negative moment at the fixed end is smaller than the positive moment of a simply supported beam.
  3. The point of inflection (zero moment) of a simply supported beam is at the end while the point of inflection of a fixed end beam is a few distance away from the support.
SHEAR AND MOMENT DIAGRAMS OF SIMPLY SUPPORTED AND FIXED END BEAMS
Based on these properties, we can point out the advantages and disadvantages.


A. Simply supported 
  1. Since there is no bending moment at the support, the joint or support is not complicated. We can simply use a shear plate or a clip angle that would resist the shear. 
  2. For rigid supports, beams can be simply laid over with no fixing. This especially applies to temporary structures during construction. Elevated concrete highways are designed as simply supported beams.
  3. The supports of the beam must be rigid. A frame with two columns and a simply supported beam on top must have columns that are moment resisting at the base. 
  4. Simply supported beams are of little help in resisting lateral forces like wind and earthquake.
  5. Simply supported beams are usually thicker due to a big value of maximum bending moment at the center.
SIMPLE SHEAR CONNECTION
Simple shear connected beams are designed as simple beams

B. Fixed End
  1. Fixed end connections are more rigid. If you are avoiding vibrations and movements at the beam, it is best to design the beam to be fixed at the end. 
  2. Designing a beam in a steel frame as fixed end eliminates the need for moment resisting base. That explains the shape of PEB frame columns that are thicker at the top and thinner at base. That also explains why sometimes, you see only two bolts at the base of the column and see twelve bolts at the joint of the beam and the column.
  3. Fixed end beam connections are moment resisting and therefore more costly than simply supported beam connections.
  4. Fixed end beams are thinner than simply supported beams because, aside from beam center, the ends are also resisting moment.


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