Page 309 - Physical Principles of Sedimentary Basin Analysis

9.2 Flexure from a point load 291

Kauai
(5.1 Ma) Hawaiian arch
Oahu
(2.6−3.7 Ma)
Molokai
(1.8−1.9 Ma) Maui Hawaiian trough
(0.8−1.3 Ma)
Hawaii
(0.0−0.5 Ma)

200 km

Figure 9.6. A sketch of the Hawaiian island chain with the flexural trough and the flexural arch.

0
x x 1
−0.20
0.00

0.20
w/w max [−] 0.40

0.60

0.80

1.00
−6.0 −4.0 −2.0 0.0 2.0 4.0 6.0
x [−]
Figure 9.7. The flexure of a plate from a point load at x = 0.

V 0 = 2 gαw max (9.38)

which says that the point load corresponds to the weight of the material in the area 2αw max
when it has the density . It also follows from the force balance (9.32) and the maximum
deflection (9.35) that