Question 2.2: The Washington Monument (Fig. 1a) stands 555 ft high and wei......
The Washington Monument (Fig. 1a) stands 555 ft high and weighs 181,700 kips (i.e., approximately 182 million pounds). The monument was made from over 36,000 blocks of marble and granite. As shown in Fig. 1b, the base of the monument is a square that is 665.5 in. long on each side, and the stone walls at the base are 180 in. thick.
Determine the compressive stress that the foundation exerts over the cross section at the base of the monument, assuming that this normal stress is uniform.
From the free-body diagram in Fig. 2, the total normal force on the base of the monument is equal to negative of the weight of the monument, so
∑ F = 0: F = -181,700 kips
(Note: In accordance with the sign convention for normal stress, the normal force F is taken positive in tension. The negative value for F indicates that it is a compressive force, as is clearly evident in this case.)
The cross-sectional area of the base is
A = (665.5 in.)² – (665.5 in. – 360 in.)² = 349,600 in²
Therefore, from Eq. 2.2,
σ_{avg} = \frac{F}{A} Average Normal Stress (2.2)
σ_{avg} = \frac{F}{A} =\frac{181,700 kips} {349,600 in^2} = -519.8 psi
Rounded to three significant figures, the average normal stress on the cross section of the monument at its base is
σ_{avg} = 520 psi (C)
where the (C) stands for compression. This is a very low stress, even for stone. Figure 3 illustrates how this uniform compressive stress would be distributed over the foundation at the base of the monument.
