Torsion & Warping Constant

[Redtelis]

Is there a free calculator for torsion and warping constant for a hollow rectangular section?

Thnaks!

 

[jayrod12]

The information you need is generally in your design code. If I remember correctly there is no warping constant for hollow steel sections. Cw=0.

 

[Hokie93]

The AISC Steel Construction Manual includes values of the torsional constant (J) for typical rectangular and square HSS shapes. If you must calculate the torsional constant, an equation can be found in any number of quality references such as AISC Design Guide 9, Roark's Formulas for Stress and Strain, and Design of Welded Structures by Blodgett. Rectangular closed sections don't warp for all practical purposes so Cw = 0, as jayrod indicated.

 

[Agent666]

If you know python this is hands down the most comprehensive free tool for determining section properties of any shape imaginable.

Plenty of examples within the documentation to get you up and running. Alternatively provide details of your section and I'll post some code to get you up and running.

 

[Redtelis]

@Agent666

It's a RHS 150x50x3.2....depth=150 width=50 and thk=50 (everything in mm).

 

[Agent666]

Hi Redtelis

The following python code will calculate all the section properties for an RHS, you didn't say what external radii you had at the corners. But assuming 2.5 times the thickness gives you the following output

import sectionproperties.pre.sections as sections
from sectionproperties.analysis.cross_section import CrossSection

d = 150  # depth
b = 50  # width
t = 3.2  # wall thickness
r = 2.5 * t  # external radii
n_r = 10  # number of points considered around curves
mesh_area = 2.5  # max mesh size

geometry = sections.Rhs(d=d, b=b, t=t, r_out=r, n_r=n_r)
geometry.clean_geometry(verbose=True)
mesh = geometry.create_mesh(mesh_sizes=[mesh_area])
section = CrossSection(geometry, mesh)
section.calculate_geometric_properties()
section.calculate_plastic_properties()
section.calculate_warping_properties()
section.plot_mesh()

# this will display all results
# check [URL unfurl="true"]https://sectionproperties.readthedocs.io/en/latest/rst/post.html[/URL] for definitions
section.display_results(fmt=".3f")

# this will specifically display torsion and warping constants
J = section.get_j()
I_w = section.get_gamma()
print(f"J = {J}")
print(f"I_w = {I_w}")

Section Properties:
A        = 1203.227
Qx       = 90242.050
Qy       = 30080.683
cx       = 25.000
cy       = 75.000
Ixx_g    = 9872587.823
Iyy_g    = 1301129.088
Ixy_g    = 2256051.241
Ixx_c    = 3104434.101
Iyy_c    = 549112.007
Ixy_c    = -0.000
Zxx+     = 41392.455
Zxx-     = 41392.455
Zyy+     = 21964.480
Zyy-     = 21964.480
rx       = 50.795
ry       = 21.363
phi      = 0.000
I11_c    = 3104434.101
I22_c    = 549112.007
Z11+     = 41392.455
Z11-     = 41392.455
Z22+     = 21964.480
Z22-     = 21964.480
r11      = 50.795
r22      = 21.363
J        = 1595225.449
Iw       = 328787528.090
x_se     = 25.000
y_se     = 75.000
x_st     = 25.000
y_st     = 75.000
x1_se    = 0.000
y2_se    = 0.000
A_sx     = 165.202
A_sy     = 870.503
A_s11    = 165.202
A_s22    = 870.503
betax+   = 0.000
betax-   = -0.000
betay+   = 0.000
betay-   = -0.000
beta11+  = 0.000
beta11-  = -0.000
beta22+  = 0.000
beta22-  = -0.000
x_pc     = 25.000
y_pc     = 75.000
Sxx      = 53810.416
Syy      = 24625.050
SF_xx+   = 1.300
SF_xx-   = 1.300
SF_yy+   = 1.121
SF_yy-   = 1.121
x11_pc   = 25.000
y22_pc   = 75.000
S11      = 53810.416
S22      = 24625.050
SF_11+   = 1.300
SF_11-   = 1.300
SF_22+   = 1.121
SF_22-   = 1.121


J = 1595225.4487198484

I_w = 328787528.08964765

I'd note in practice I_w is not actually zero, however most design codes might say to take it as zero for use in respective codes lateral torsional buckling formulations as others have previously noted as hollow sections are rarely subject to lateral torsional buckling due to their high torsional rigidity (except for extreme sections with I_y much less than I_x, or when the load acts far above the shear center).

 

[BAretired]

I_w = 328,787,528.08964765 does not seem like zero but it depends on the units used. The units used in the 2004 edition of the Canadian Institute of Steel Construction (CISC) handbook are mm⁶ but for all shapes where C_w is listed, 10⁹mm⁶ is the factor at the top of the table of warping constants. That would mean, for this case, I_w or (C_w) = 0.328*10⁹mm⁶ which is small compared to other shapes. Elsewhere, CISC 2004 states "C_w = 0.0 for hollow structural sections".

Expressed in the Imperial system, Cw or I_w = 1.22 in⁶.

BA

 

[Agent666]

Sorry, yes all output is in terms of mm's, units are consistent with whatever units we're used as inputs, mm in this case for defining the section geometry. You could equally define the mesh and geometry in inches or feet or miles if you wanted and calculated output will be consistent with the chosen units system.

Agree relative to other shapes the warping constant is small.