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Can two beams intersect each other without a  column at the intersection
in Civil Engineering by  

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Yes they can intersect without a column at the intersection, 1 of the beam will be known as the primary beam and the other as secondary beam. The secondary beam will pass through the primary beam which will act as the support. You will 1st design the secondary beam before the primary beam.

Moreover, Either cantilever or proped cantilever beam could be used in such a case too.