Why are there so many different structural shapes?
And how can you find out which one is the best for a given scenario?
Wall framing is often done with rectangular wood studs, but sometimes with gauge steel
channels.
And adjacent elements are commonly connected with angle shaped clips.
Steel I or H beams are often used to support decks for long spans to create more open spaces.
But in other cases T-shaped concrete beams are used, and with round reinforcing bars.
Hollow sections are common too.
Whether round, square, or rectangular.
How can one navigate this landscape of cross sections to determine what’s best?
In this video we’ll analyze and compare these shapes to create a rating scheme
for you.
ANALYSIS CRITERIA Many shapes of cross sections exist for structural
elements, and each come with their own advantages and disadvantages.
The primary considerations for structural shapes are their area, bending resistance
(S, I), buckling susceptibility (b/t), torsion resistance (J), symmetry, and workability:
• Area is important because more area is more material, which results in more weight
and cost.
• Bending resistance is important for beam sections particularly, since this often governs
their design.
Area moment and section modulus are used to quantify bending resistance.
Area moment is higher when more material is further from the neutral axis, and more area
moment means less deflection.
Section modulus is derived from area moment and determines bending strength.
Having more material further from the centre increases both of these parameters.
• Buckling susceptibility determines how far a section or element can span before the
buckling.
Buckling can happen either globally or locally.
Global buckling depends mostly on length, but also area moment and material modulus
(i.e. stiffness).
Local buckling, on the other hand, depends on the b/t ratios of individual elements within
a section.
Higher b/t ratios mean more susceptibility to local buckling.
Axial resistance is lumped in together with buckling susceptibility for the purposes of
this analysis, since area and length are held constant.
• Torsional resistance determines how much twisting a section can take before failing
in internal shear stress or excessively rotating.
This is controlled by the torsional constant, J, which essentially measures how much area
is closed into the shape-- lots of enclosed area means torque is well resisted.
• Symmetry is an important factor for determining ease of construction and manufacturing, as
well as how a section can resist loads in various directions.
Symmetry is quantified by the # of symmetrical axes.
More symmetric shapes also have patterns that are more easily repeatable.
• Workability, will be defined here as the number of faces and vertices plus the ability
to create positive connectivity.
More workable shapes generally have fewer faces and vertices allowing connections to
be more versatile.
Positive connectivity basically means a connection can maintain nominal loads in any direction,
and this is commonly achieve by nesting elements within one another or having arrays of connectors.
We also understand that less stiff materials are much more workable, such as wood vs steel
or concrete, but we’ll save that analysis for a future video.
For our analysis in this video, we’ll take a fixed area to compare the strengths and
weaknesses of various cross sections ranked by bending, buckling, torsion, symmetry, and
workability.
We’ll analyze and compare the following sections: I or H or wide flange, rectangular
and square (solid and hollow), circular (solid and hollow), Channel, T, and Angle.
I-BEAM / W-FLANGE With most of its area far from the centre,
the I-beam is very strong and stiff in bending on its primary axis.
These sections have high area moment and high section modulus, even when taken as a ratio
of area.
Symmetry exists on two axes as well, but one direction is much weaker than the other.
That’s why I beams often have wide flanges so that they can better resist loads in both
directions, especially when used as columns or piles.
The problems with I-beams lies in torsion resistance and buckling susceptibility.
Individual elements of an I beams can be slender, indicated by high b/t ratios—this means
they’re more likely to buckle, such as a web buckling at a point of load application,
or flanges buckling from lateral loads.
In terms of torsion, the I-beam does not form a closed section, and has no continuous area
far from its neutral axis, therefore it’s very weak in torsion.
Ways around this are to add braces or stiffeners.
Check out some of our old videos for more info on this.
The I-beam also has many sides and vertices, which adds manufacturing and construction
complexity compared to say, rectangular sections.
The I-beam's score is lowest in torsion resistance, and also lowered in the buckling category
due to the tendency for web or flange elements to be slender.
Otherwise, the I-beam score quite well in the other categories.
Let’s see how the other shapes perform!
RECTANGULAR Rectangular cross-sections are relatively
convenient for construction.
They’re flat on four faces, facilitating easy installation of adjacent flush elements
such as sheathing or clip angles.
They are also easier and less wasteful to manufacture from say the cross section of
a tree, which would have a lot more waste if I shapes were cut out of them.
However, there is less use, structurally, for much of the material closer to the centre.
The bending resistance is strongest on one direction of loading (called the strong axis),
and less on the other direction—so these shapes should be oriented in the direction
of primary applied loads.
Torsional resistance is okay as long as elements aren’t too thin, since there needs to be
a continuous path for twisting at a decent distance from the shapes centre.
Symmetry exists on two axis, so workability is good—it doesn’t matter if you flip
a 2x4 upside down, for example.
b/t ratios can sometimes be an issue, such as for thin plate elements—which end up
being susceptible to buckling.
This concept is the same as the I-beam, since the I-beam is made up of several rectangular
elements.
The same comments as rectangular apply to square, but square has a bit of additional
advantage on symmetry and thus is good for conditions where loads of similar magnitude
are applied on both axes, so similar strength would be needed for loading in both directions.
Rectangular and square sections can be optimized (in some sense), by creating hollow sections
or tubes.
Hollow sections remove the material closer to the centre, which is much less efficient
structurally.
However, having hollow sections creates some additional complexity for connection points
since one sided connections or pass holes may be needed.
Solid rectangular sections score highest on workability due to their accessible flat faces,
but hollow rectangular sections get a comparative reduction on workability since their interiors
are difficult to access.
However, the hollowing out of tubes does move more area further from the centre, so hollow
sections perform much better at torsion and bending compared to solid.
CIRCULAR Solid circular shapes are ideal for local
buckling resistance.
These shapes have a minimized b/t ratio since diameter is constant for a circle.
However, these shapes have a lot of area bunched up towards the centroid; since this material
near the centre is less structurally efficient, the circular shape can be optimized in some
sense by moving the area away from the centre to create the pipe section, which has much
higher area moment (and thus bending resistance)—but is more difficult to construct and work with.
Circular shapes, both solid and pipe, are good at resisting torsion because these shapes
have a continuous path far from the shape’s centre to resisting twisting loads.
Pipe sections are better at this since, again, the material closer to the center is not as
structurally efficient.
Offsetting this however, is the fact that pipe sections can have local buckling issues
if they are too thin.
Pipes sections are ideal for resisting forces from fluid pressures within, since they have
no corners which avoids discontinuities that cause increased local stresses.
However, pipes are mediocre at resisting bending stresses, since a significant portion of material
is close to the neutral axis.
Difficulties with circular sections do arise however with constructability.
Since circular sections have no straight sides for attachment, special connectors are needed.
For pipes this takes form in pipe collars, flanges, hangers, and other splice details.
For circular concrete columns this means curved hardware at connection points.
For ropes and cables this means clamps, sleeves, and splices.
And for Rebar, this means having deformed bars to transfer loads at the interface to
concrete being poured around.
circular sections score the worst in workability because they have no flat faces for attachment,
but they score high in torsion and buckling resistance because of their lack of corners
and continuous area far from the center.
Symmetry is also maximised since these sections are symmetric about any axis through their
centers.
CHANNEL Channels sections are, in essence, half of
I beams cut vertically.
This gives them one axis of symmetry.
Channels have the advantage of other components being able to be nested inside them, making
them particularly good for positive connectivity.
Some examples of this are Unistrut and anchor channels.
Channels are also used for steel studs, allowing for tracks which can sometimes be slotted
for deflections.
Channels are often used for glazing too, making little pockets for the glass to fit into.
Structural steel channels are also common for edge beams and other cases where having
flat face for attaching flush elements is advantageous.
Channel sections are even sometimes augmented to have slanted flanges and large lips, which
we often hear referred to as ‘hat tracks’.
Channels have only part of the bending resistance advantage of I-beams, because even though
they have material far from the neutral axis, they only do so with flanges on one side.
Channels generally share the same flaws as I-shapes in terms of torsion and buckling
susceptibility as a result of being an open section.
The workability score of channels makes them stand out in comparison to most other shapes.
Channels primarily receive their high workability score from allowing components to be nested
within one another, thus providing positive connectivity
TEE Tee shapes are, in essence, half of I-beams
cut horizontally.
This gives them one axis of symmetry.
These shapes are most useful for simple bending about one axis and in one direction—for
this purpose T-shapes share the advantages of I-beams, but are less versatile since they
often can’t take much load reversal or lateral loading.
Some examples of T shapes are T-bar ceiling, double-T precast concrete, and certain types
of slab edge connections.
In some of these types of situations T-shapes can be quite practical for flush mounting/dropping
on elements because of their accessible flat faces.
Like channels, T-shapes generally share the same flaws as I-shapes in terms of torsion
and buckling susceptibility as a result of being an open section.
ANGLE Angles are often used to clip elements together
locally, and are common at connection points.
These are favorable for attaching two elements, each being fastened to one leg or flange.
Angles are not favourable for bending or torsion, since they essentially have all the flaws
of the I-beams with little of the advantages.
Even for connections, angles can sometimes be too weak against bending or buckling and
are often seen with gussets to strengthen them.
Although angles technically have one axis of symmetry, this axis is diagonal and it’s
generally not practical to span an angle in this way—so angles effectively have no useful
axis of symmetry.
Sometimes angles are doubled up or butted together, to form Z’s or T’s, which gives
them additional versatility and workability points.
the angle section's score is almost completely from workability.
Angles are very useful for connections, but not great at spanning like the other sections
RESULTS AND DISCUSSION The variety of structural shapes can make
it difficult to know which one is best for a given scenario.
Based on our analysis, the wide flange I-Beam comes out on top as the best shape.
However, we should keep in mind that certain shapes are simply best suited for particular
applications, and other factors such as material and area could be factored in.
If cost is less of a factor, maybe it’s not an issue to increase area to offset some
flaws.
Or, maybe certain drawbacks can be avoided by using alternate materials.
Reinforced concrete is particularly innovative example of note here:
Concrete sections can be rectangular, T-shaped, L-shaped, I-shaped, or even circular.
And beyond that, they have embedded circular reinforcing bars placed where such elements
are most effective.
Similarly, Even standard wood framing can be viewed in a similar light, since wood framed
walls and floors being sheathed transform from simple collections of rectangular sections
into repeating patters of T or H sections.
CONCLUSION AND ADVERTISEMENT We hope this video gives you a helpful understanding
of various structural cross-sections, and we welcome questions and discussions in the
comments below!
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