# shear flow in hollow beam

for shear flow at D , the Q = Ay , i tried another method , i gt 30000 , instead of 29750, why the ans is different from 29750? why cant i use this method( i break the shaded area into 3 parts ( as shown in figure) my working is Q = Ay = (60x10x35) + (2x30x10x150) = 30000  Is my working not acceptable ?

## 1 Answer

Acceptable for what? For practical engineering purposes it would usually perfectly acceptable. The difference between the two values is less than 1%.

The book is making more "precise" assumptions (see the plot of the shear distribution in Fig. e) but the author might have "forgotten" that all of this mathematical theory is based on approximations (Euler-Bernoulli-Timoshenko beam theory) in any case!

The "correct" answer depends on exactly how the shear loads are applied to the beam and how it is supported - both of which are ignored in the book example.

Of course in some situations you might need to do a full 3-D finite element analysis of the hollow structure to get even more details of the stress distribution - but that would be pointless if it is just being used as a structural beam and you don't know exactly how it is loaded and restrained.

• sorry , i want the accurate ans ... you can noticed that i made different cut with the author . In my working, i cut the flange at it's bottom part , whereas in the author's wroking , he cut the flange at its sides...Which is correct ? – kelvinmacks Nov 27 '16 at 0:01
• They are both approximations within the expected error for this problem. I don't know if we can easily determine which is more accurate. – JMac Nov 28 '16 at 12:14