A concrete foundation wall will be subjected to a lateral soil pressure of 45 psf per foot of depth. If the wall is 8 feet high, what is the total lateral force per linear foot at the base of the wall?
Correct Answer
D) 1,440 pounds per linear foot
Lateral pressure increases linearly with depth. At 8 feet deep, pressure = 45 × 8 = 360 psf. Total force = (360 psf × 8 ft) ÷ 2 = 1,440 pounds per linear foot.
Why This Is the Correct Answer
Lateral soil pressure increases linearly from zero at the top to a maximum at the base. The pressure diagram is triangular. Maximum pressure at 8 ft depth = 45 psf/ft × 8 ft = 360 psf. The total lateral force equals the area of the pressure triangle: (base × height) / 2 = (360 psf × 8 ft) / 2 = 1,440 lb per linear foot. This is the resultant force acting at one-third the wall height from the base.
Why the Other Options Are Wrong
Option A: 2,880 pounds per linear foot
2,880 lb/ft would result from using the full rectangular pressure (360 psf × 8 ft = 2,880 lb/ft) without dividing by 2. This error ignores the triangular distribution of lateral earth pressure — pressure is zero at the top and maximum at the base, not constant throughout the depth.
Option B: 360 pounds per linear foot
360 lb/ft is only the maximum pressure intensity at the base (45 × 8 = 360 psf), not the total force. Confusing pressure (force per unit area) with total resultant force is a common calculation error.
Option C: 180 pounds per linear foot
180 lb/ft would result from dividing 360 by 2 without multiplying by the wall height first. This incorrectly treats the pressure value as the total force rather than computing the triangular area correctly.
Memory Technique
Think of the pressure diagram as a right triangle: the height is the wall height (8 ft) and the base is the maximum pressure (360 psf). Area of triangle = ½ × base × height. The phrase 'Triangle Halves the Total' can remind you to always divide by 2 for linearly increasing lateral pressures.
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