Page 373 - statbility for masters and mates

Example
A deck beam is in the form of an H-girder as shown in the accompanying Figure 43.4.
Bending and shear stresses 361
Fig. 43.4
If the bending moment at the middle of its length is 15 tonnes metres, ®nd the maximum stress in the steel.
I BH3 2bh3 12
I 30 303 2:14:253 12
I 810 000 437 500 12
I 372 500 cm4 12
f MI E y
y H 30 15 cm
22
f 1500 12 15
Ans. Max. Stress 0:725 tonnes per sq cm or 725 kg per sq cm
The above theory can now be used to ®nd the section modulus of the ship. The external bending moment can be calculated, as can the stress at the transverse sections under the conditions of maximum bending moment. The neutral axis passes through the centre of gravity of the section and, because of this, its position can be found. The moments of inertia of all of the continuous longitudinal material about this axis can be found. Then the section modulus is equal to I/y.
Shearing Stresses
It has already been shown that a shearing stress across one plane within a material produces another shearing stress of equal intensity on a plane at right angles. (See Complementary Stresses in Chapter 40.)
The mean shearing stress in any section of a structure can be obtained by
372 500
f 0:725 tonnes per sq cm