PE Civil Practice: Eccentrically Loaded Wall Footing

NCEES Civil PE Specification Soil Mechanics: Bearing capacity

Problem

A wall footing is situated 3 ft deep within a sand layer, as illustrated in the figure. The width of the footing is 5 feet.

The superstructure loads include:

Concentric load: \(12\ kip/ft\)
Moment: \(15\ kip-ft/ft\)

The maximum soil pressure \((lb/ft^2)\) per foot of wall under the footing is most nearly:

Select an Answer:

A) 6,400
B) -1,200
C) 6,000
D) 6,750

% Students Correctly Answered:

71.2%

Solution

Eccentricity is expressed as \(e = M/P = 15/12 = 1.25\ ft\). To assess the effectiveness of the entire footing width, a comparison is made between the eccentricity and \(B/6\), where B denotes the footing width.

With \(B/6 = 5/6 = 0.83\ ft\), it is observed that the eccentricity (\(1.25\ ft\)) exceeds \(B/6\).

Given that the eccentricity is greater than B/6, the resultant load does not fall within the middle third of the footing base. Consequently, this situation leads to uplift on the far side of the footing.

The maximum soil pressure is determined by:

\[q_{max}=\frac{4P}{3L\left(B-2e\right)}\]We are calculating the pressure on a wall footing, so consider unit length L = 1:

\[q_{max}=\frac{4P}{3\left(B-2e\right)}=\frac{4\times 12}{3\times \left(5-2\times 1.25\right)}\times 1000=6,400\ psf\]The pressure noted above is per foot of wall.

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Practice Question: Eccentrically Loaded Wall Footing - Uplift

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