Page 372 - statbility for masters and mates

360 Ship Stability for Masters and Mates
Since E and R are constant, then:
M RE Sy2 dA
But S y2 dA is the second moment of the area of the section about the neutral axis. Let S y2 dA be equal to I.
; M RE I
Now if f is the stress at a distance of y from the neutral axis, then:
or But
and
f Ey R
RE yf MI RE
; yf MI f M
I/y
The expression I/y is called the section modulus, designated Z, and attains its minimum value when y has its maximum value. The section modulus is the strength criterion for the beam so far as bending is concerned.
Example
A steel beam is 40 cm deep and 5 cm wide. The bending moment at the middle of its length is 15 tonnes metre. Find the maximum stress on the steel.
lb3 I 12
5 403 12
I 80 000 cm4 3
M
f I y
y d 40 20 cm 22
So
f 1500 3 20 tonnespersqcm 80 000
f 1:125 tonnes per sq cm
Ans. Maximum Stress 1:125 tonnes per sq cm or 1125 kg per sq cm