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RE: Structural Engineering Rules of Thumb

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Several years ago, make that many years ago (red book), I worked out the formulas in the AISC beam diagrams to calculate deflection based on moment.  I worked it out for moment to be in k-ft and length to be in feet.  These are easy formulas to remember.  I copy them over every time I get a new AISC book.


Uniform load

Delta=5wl^4/(384EI)  For steel this is Delta=(M*L^2)/(161*I)  For any other material it is delta=(180*M*L^2)/(E*I)


Point load in middle

Delta=Pl^3/(48EI)   For steel this is Delta=(M*L^2)/(201*I)


For a center peak triangular load

Delta=(W8l^3)/(60*E*I)  For steel this is Delta=(M*L^@)/(168*I)


And I did this for several more load cases.  What is interesting is the Uniform load produces the highest deflection.  It has the smallest denominator constant.  So, if you want a quick conservative deflection check, not matter what the actual loading is, the Delta=(M*L^2)/(161*I)  will give you the largest deflection possible.


Reverse Delta and ‘I’ and you get quick equations to calculate minimum ‘I’ required for a deflection ratio limit.


I usually have my results from analysis in k-ft & ft so these formulas are very handy.





From: G Vishwanath [mailto:gvshwnth(--nospam--at)]
Sent: Friday, February 05, 2010 5:30 AM
To: seaint(--nospam--at); steel steel
Subject: RE: Structural Engineering Rules of Thumb



Thanks for this initiative in the seaint list

Let me also make a humble contribution.


Here is one rule of Thumb I have found useful during may years as a designer of steel structures.


If you need to do a quick check of the maximum deflection of a steel beam subjected to some udl and some  point loads, you can use the following easy formula


defln = M x L^2 / (10 x E x I)


M = max BM

L = span

E = Elastic modulus

I = Moment of Inertia.

Take care to use a consistent set of units.

You will be surprised to note how close you are to the exact value if you do a rigourous calculation. This is for beams with a mix of udl and a few point loads scattered here and there along the span. Don't use this for a standard beam with a standard udl only or beams with just one point load. You can use it with beams with three or more point loads and some udl of partial udl.