Hyperfine Cantilever Answer See written answer as PDF
first find the area of the triangle. A= 1/2 x BH
the height of tbe cantilever was given (H= 9'-0") and the base would be the soil pressure multiplied at thw height we are looking for, in this case we are looking for 9'-0". B= 30#/ft3 x 9'-0" -> 270#/ft2
A= (9ft x 270#/ft2)/2
A= (2430#/ft)/2= 1215 #/ft
Now that we know the area, we still have to determine what the pressure is at the location we want. To do this, we have to figure out what the pressure is at 1 linear foot. P= A x 1ft -> 1215 #/ft x 1ft -> 1215#
The next part of the question asked to determine the overturning moment at 1/3 the height. OTM = 1/3 x 9' x 1215# -> 3645 ft-lbs
where would you place the rebar? the answer is always where tension would occur. Concrete's strength is with compression but it's weakness is in tension therefore rebar is meant to assist. As you see in the image, the moments have been identified along with the tension side. Could the rebar be located on both sides of the cantilever? absolutely, but the most efficient and effective method for rebar based on the requirements for the question is shown.
Why does the horizontal rebar extend the length of the footing? Why does the vertical rebar come down through the footing and extend horizontally in one direction?
The answers to both of these is development lengtb
. By embedding the rebar in concrete, it can't get the full strength so instead lengthening it allows the rebar to gain additional strength from the compressive side to assist on the tension side by providing more resistance.
if you can remember the equation, the math could be done quickly, but you may want to come back.