# Why can't I-beam resist torsion but can resist shear stress due to transverse loading?

It is already known that the I-beam is very bending resistant (causes less deflection for the same transverse load and also results in lesser stresses relatively). But for an eccentric transverse load (i.e. the line of action of load does not pass through the axis of the beam), the I-beam can also be subjected to torsion. And it is believed that I-beam are not very strong in torsion.

Can anyone point out the reason that why I-beams are not very resistant and strong in torsion, but when subjected to a transverse load, they can resist the transverse shear stress? What is the difference between the shear stresses coming from torsion and coming from tranverse loading?

• How does the shape support the loads? Nov 8, 2021 at 11:25

IMHO the most important issue, is that the IPE cross-section is considered an open section with respect to torsion. This reduces the resistance to torsion significantly.

Figure : Shear stress due to pure torsion of an I beam (source AISC seminars)

In essence the effect can be observed easier if you take a straw and cut it open along its length.

Then take another straw and compare the behaviour between the original straw (closed section) and the "gutted" straw (open section)

Figure: Shear stress distribution of Close vs open thin wall section under shear stress (source Holooly)

Another reason, is that the torsional response is governed by the polar moment of area ($$J_p$$) instead of the second moment of area ($$I_{xx} ,I_{yy}$$).

And while these are related , i.e. $$J_p =I_{xx} + I_{yy}$$, the torsional response is affected for the I beam.

E.g. In the following table:

for IPE80 the

$$I_{xx}$$ $$I_{yy}$$ $$J_{p}|$$
IPE 80 80 8.49 ~84.5
IPE 160 869 63 ~935
IPE 240 3892 283 ~4175

You might notice a trend that the $$I_{xx}$$ is over 10 times larger than $$I_{yy}$$ and that trend intensifies for larger dimension.

• Consider the broken straw example that you provided. If I re-join the straw (from the region where it was cut) using glue, for example, so will it still work when subjected to torsion like it did when it was a continous body (with no cut)? Nov 9, 2021 at 9:00
• Yes it would approximate the undamaged behaviour. Nov 9, 2021 at 10:34