ARE Horizontal Shear Forces
ARE structural question
Question 21 Answer See written answer as PDF
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.