Rectangular Hollow Section beam calculator

This is solely an Euler-Bernoulli beam [Wikipedia] leading into simple "Moments sum to zero" calculator.

It knows nothing of design codes (eg the "EN 1990" series of the "Eurocodes").
What this calculator does is: [links are to Wikipedia]; {are the input variables}
I {dimensions} → Z → M_y {σ_y} → M=FL or M=FL/4 {L}

* Use SI units * You can use indicial notation
eg 123.45mm == 1.23453e-1m == 123.45e-3m

My calculation is based on a "sharp" right-angled-corner shape.
In the real world Rectangular Hollow Sections have curved corners.
The deviation caused by this from real sections is small - but there.

Authoritative tabulated data for commercial sections including important characteristic which cannot be readily calculated are presented as The Blue Book - Steel for Life [external link] which is considered a vital information for most working with steel.
The program might allow you to rapidly explore concepts, but The Blue Book - Steel for Life [external link] needs to be your reference.

Step-by-step guidance for finding the maximum load and deflection just before onset of yielding (bending) for a "regular" RHS

If you have a "regular" commercial Rectangular Hollow Section beam the "steel properties"

"RHS material Young's modulus" - any structural steel, regardless of yield stress, can be taken as having a Young's Modulus "E" of 210GPa - for which you enter 210e9
"RHS material yield stress" - the steel will be specification "S355", with a yield stress of 355MPa - for which you can enter 355e6 (in the rare case of the beam having a higher yield stress steel the answer will be conservative ("to the safe side")).

Beam dimensions, known by measurement, are entered here in the SI unit of metres. Hence "100mm" is entered as 100e-3, etc.
A representative example features in the mechanical tests in
Weld test - weld at centre of centrally-loaded simply-supported beam
(the presence of the butt-weld (seam-weld) is irrelevant to the calculation).
The commercial section is the nominal 100x50x8mm RHS.
The accurately measured wall thickness of 7.8mm is used in this calculation and the linked example. The difference between nominal and accurately measured wall thickness is within-tolerance and negligible (too small to matter) given all other uncertainties like the effect of corner radius, etc.
For the 100x50x7.8mm RHS which is 0.6m between bearers (end-supports), enter

100e-3 for Height
50e-3 for Width
7.8e-3 for Wall-thickness
0.6 for beam length

then

355e6 for yield stress
210e9 for Young's modulus

Your "real" input form should then look something like this:

Clicking on "Submit", the answer includes:

Second Moment of Area = 2.443193e-6m^4 (244.31934592cm^4) [244cm^4]
Moment = 17346.6735603 (N.m) [17.3kNm]
For a "simple beam" (it's supported at the ends, with a point central load), that central load on reaching the yield stress is 115644.490402Newtons [116kN]
The deflection is 0.00101428571429metres (1.01428571429mm) [1.0mm]

"The Blue Book" gives for a commercial 100x50x8mm RHS a Second Moment of Area of 230cm^4. Which agrees with the calculated 244cm^4, allowing for the real commercial section having rounded corners, which slightly reduces the Second Moment of Area
Moment resistance "Mc,y,Rd" is given as 21.8kNm. Which is somewhat higher than calculated "Moment" of 17.3kNm. That calculated "Moment" is "Moment resistance" given the "Maximum stress" has been set to the yield stress of 355MPa.
The calculated "Maximum stress" and "deflection at the middle of the beam" are "extrinsic", dependent on the length of the beam, so are not tabulated in "The Blue Book".
But are seen, with "arithmetic workings", in the linked page.
In that page "F_max=115644 N" [116kN] and "y=1.014286e-03 m" [1.0mm] - which agree with output of the online beam calculator.

The arithmetic in this online beam calculator to find the deflection as well as the load is thought to be novel (?), and is presented here. In one of the pages linked from there is discussion showing that it is very safe to assume that any Rectangular Hollow Section encountered in structural steelwork has a yield stress of 355MPa.
Please use the Contact form to alert me if you know of any case where this is not correct.

(R. Smith, 24Jul2023, 03Aug2023 (title), 12Feb2024 (worked example), 13Feb2024 (eg. form))