ARE Horizontal Shear Forces

ARE structural question

Question 21 Answer

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The answer is 2.5k.

Col 2 has twice the number of rigidly connected beams framing into it as cols 1 and 3. Therefore it attracts 2x the load of the outer cols.

More beams = more stiff = attracting more load. The total base shear is the sum of the lateral loads, so 5k.

The sum of the col shears needs to match this, so V1+V2+V3=5k. Since everything is spaced evenly and the cols are the same stiffness we can solve for in terms of V. V1=V2=V and V2=2V.

Plugging these into the earlier equation, V+2V+V=5k. So V=1.25k and therefore V2=2.5k.

if you can remember the equation, the math could be done quickly, but you may want to come back.