Content uploaded by James Dingley
Author content
All content in this area was uploaded by James Dingley on Apr 09, 2025
Content may be subject to copyright.
Structural Optimization of I-Beams via Typographical Analysis: A Comparative Study of
Alphabetical Cross-Sections
James Dingleya, Prof. Kerri Cahoya
aDepartment of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge 02139, MA, USA
Abstract
Recent advances in computational mechanics and manufacturing technologies have enabled the exploration of unconventional cross-
sectional profiles in structural engineering. One such profile—long assumed to be optimal—is the I-beam, named after the capital
letter “I” which its wide flanges and thin vertical webbing resemble. However, the typographic origin of this nomenclature remains
unexamined in structural terms. This study investigates the structural performance of capital letterforms from over 1,000 digital
typefaces to determine their suitability for use as beam cross-sections under bending. A custom simulation pipeline employing finite
element analysis was developed to automate mesh generation from typographic contours, with results normalized for beam mass to
allow direct comparison. Experimental validation was conducted using physical beams machined from high-density polyethylene
and tested on an Instron load frame. Simulated and real-world data revealed that several typefaces outperform the conventional I-
beam under specific loading conditions. Under observation that a rotated “H” also resembles an I-beam profile, additional analysis
was conducted into the performance of not only this rotated “H” but also the rest of the alphabet. To reflect how I-beams are today
employed in more than just simple bending, this full set was also examined in the buckling, tension, and torsion regimes. Notable
results are that the ( ) typeface produces an I-beam that is most similar in form and appearance to a regular I-beam
and ( ) performs slightly better due to the efficient removal of fillets in favor of wider flanges. Considering other
letter-forms, rotated “H” profiles exhibited superior performance in both bending and torsion, while circular forms such as capital
O provided the best resistance to buckling. In contrast, handwritten fonts such as ( ) [Zapfino] tend to fail prematurely, with
letters such as J and L present insufficient cross sectional support. This study not only challenges long-standing assumptions about
I-beam geometry but also demonstrates the potential for incorporating typographic diversity into functional structural elements. All
code, data, and analysis tools have been made publicly available to support future work in typographic engineering.
Keywords: I-beam, Typeface, Structural Analysis, Finite Element Method, Typography
1. Introduction
The beam bridge—exemplified by a fallen log across a
stream—is among humanity’s oldest engineering inspirations.
Since the Neolithic era, the civic-minded Homo sapiens likely
understood that while a larger log might provide a sturdier span,
a carefully chosen smaller one could deliver adequate strength
while being far easier to transport [1]. The masons of Egypt’s
Old Kingdom refined the rectangular lintel, while those of Ar-
chaic Greece developed the cylindrical pillar [2]. Although
these forms were once ubiquitous, today’s structural engineer
instead relies on the I-beam: a profile characterized by two hor-
izontal flanges joined by a vertical web and named for its re-
semblance to the ninth letter of the Latin alphabet (Figure 1).
While the I-beam provides excellent resistance to bending, effi-
cient mass distribution, and high rigidity, it was never designed
for optimal performance. Rather, it emerged from the demands
of early rail infrastructure, its shape dictated by the capabilities
of 19th-century steel rolling mills [3].
This leads to the central question of this paper: Could the I-
beam be improved? And might that improvement come in the
form of a capital letter “I” from an existing typeface?
Figure 1: A selection of I-beam profiles (L to R) in , ,
and as compared with a traditional IPE100 beam.
1.1. The Origins of Typography
Typography traces its roots to 1447 with Johannes Guten-
berg’s movable-type printing press. His fonts replicated the
dense, ornate script of monastic calligraphy—an aesthetic now
known as a [4]. In 1470, Nicolas Jenson introduced
as a more legible alternative [5]. Over time, typefaces
diversified: some retained a handwritten feel ( ), others
prioritized legibility ( ), and still others embraced
pure artistic flair ( ) [6].
To satisfy both technical accuracy and the inevitable pedant,
we must distinguish between fonts, typefaces, and classifica-
Preprint submitted to Engineering Structures April 9, 2025
Figure 2: Fundamental principle of beam rolling (L) and application to the I-
beam (R). Adapted from [8].
tions. A font is a specific style and size of a typeface—e.g.,
Computer Modern Regular at 10pt differs from Computer
Modern Bold at 10pt and from Computer Modern Regular at 5pt. A typeface
is a family of fonts with a consistent visual style. For example,
and are different typefaces. Typefaces are
further categorized into classes such as Serif ( ,
), Sans Serif ( , ), and Handwritten ( ,
). In this paper, we shall use these terms interchange-
ably and unapologetically.
1.2. The Mechanics of I-Beams
While structural beams have been used for millennia, the I-
beam arose during the Industrial Revolution in response to new
manufacturing techniques and infrastructure demands. The de-
velopment of rolling mills by Robert L. Stevens and William
Fairbairn in the 1830s and 1840s allowed iron and later steel to
be shaped into long, standardized profiles [2]. Unlike the ear-
lier practice of individually casting track sections, rolling pro-
duced stronger, more fatigue-resistant members with improved
surface finish and fewer defects [7]. Figure 2 illustrates how a
section of steel is shaped between rollers to form an I-beam, a
shape born directly from the constraints of this process [8].
The I-beam’s structural efficiency arises from its geome-
try. As shown in Figure 3, under bending, the material above
the centroid is in compression, while the material below is
in tension. These stresses peak at the upper and lower sur-
faces—precisely where the flanges concentrate material. Mean-
while, the central web, which experiences relatively little stress,
is made thinner to conserve mass. This design provides strength
where it’s needed most, resulting in an excellent strength-to-
weight ratio.
1.3. Approaches to Structural Analysis of Beams
Efforts to improve the I-beam continue, often through
changes in geometry or materials. The simplest structural anal-
ysis involves calculating the second moment of area:
I=πr4
4,(circular cross-section) (1)
I=a4
12 ,(square cross-section) (2)
I=ZA
y2dA,(general case) (3)
Figure 3: I-beam in three-point bending. Load is applied at point 1 and resisted
by reaction forces at points 2 and 3. The outer flanges A and C carry compres-
sive and tensile stresses, respectively, while the inner web B remains relatively
unstressed.
Such formulas are common in engineering texts [9]. Though
tempting, optimizing beams purely via these equations over-
looks real-world limitations like stress concentrations, local
buckling, and asymmetric geometries [10].
Experimental testing has long guided beam design. In
the 1930s, Stevens and Fairbairn iteratively improved designs
through hands-on fabrication and load testing [2]. More re-
cently, Chandra et al. (1991) fabricated and tested thin-walled
laminated I-beams for aerospace use, using an Instron machine
to measure bending and torsional performance [11].
Computational methods add further insight, though they
should be validated against physical data. Liam et al. (2012)
tested cold-rolled steel beams to failure using a hydraulic press,
while also simulating the same profiles in ABAQUS—a popular
finite element software. The simulations matched experimental
results closely, albeit conservatively [10]. Fr˘
atit
,a et al. (2018)
[12] compared I- and H-beam designs for automotive connect-
ing rods using Autodesk simulations alone, demonstrating an-
other pathway to design insight without physical testing.
1.4. Approach
Where prior work has refined I-beams through incremental
improvements in material and manufacturing, this paper takes
a different path. Here, we abandon logic, practicality, and cost
to ask a bold question: Could an optimal I-beam shape already
exist, hiding in plain sight among the capital letter “I”s of type-
faces?
We test a range of typefaces using both experimental and
computational methods. To the best of the authors’ knowledge,
this is the first attempt at structural optimization of I-beams via
typographical analysis.
2. Methods
This section outlines the physical experiments and computa-
tional simulations used to evaluate typographic I-beams. After
testing several manufacturing methods, CNC milling in HDPE
was chosen as the most consistent and repeatable approach. Ini-
tial lab tests were performed on a standard IPE100 profile and
2
Figure 4: Resultant tooling path for ( ). Material is removed by
tool B from the original block around C, with the ends A and C retained for
mounting. Colors represent successive tooling passes. Note that here we use
a 60 mm ×120 mm stock block rather than the full 120 mm ×120 mm. This
is because is taller than it is wide, allowing the team to save material and
machining time by using narrower stock.
several representative fonts. These were used to validate a cus-
tom finite element analysis pipeline capable of evaluating hun-
dreds of beam designs. Finally, the best- and worst-performing
beams from the simulation dataset were fabricated and tested in
bending to confirm the model’s accuracy.
All fonts were sourced from standard Microsoft Windows
(192 typefaces) and Apple macOS (353 typefaces) licenses,
supplemented by the top 1000 typefaces from Google Fonts.
2.1. Profile Design and Scaling
All beams were based on capital letters from various digi-
tal typefaces. While particular attention was given to the “I”
character—and the rotated “H” character, which shares a simi-
lar form—the entire alphabet was examined with the same level
of scrutiny. Since fonts vary widely in dimension, each glyph
was scaled to fit within a 120 mm ×120 mm square to match
the available HDPE stock. Of the 600 mm total length, only
the central 500 mm of each beam was shaped; 50 mm was left
untouched at either end for fixture mounting (Figure 4). To pre-
vent unfair advantages for designs with more material, results
were normalized against beam mass. This ensured that beams
filling more of the bounding box did not automatically outper-
form others by sheer volume alone. These assumptions were
applied in both physical and computational testing to ensure
consistency and comparability across methods.
2.2. Physical Fabrication and Testing
While hot rolling is the standard method for producing steel
I-beams, the scale and cost of setup made it impractical for
small-batch production. As shown in Figure 5, early attempts
using 3D-printed PLA failed due to delamination along layer
lines, which made print quality—not geometry—the primary
determinant of strength. Wood was explored as an alternative
but was found to be inconsistent in both density and grain di-
rection. The chosen material was high-density polyethylene
Figure 5: Initial material bending tests for a wooden ( , top) and 3D-
printed PLA ( , bottom).
Figure 6: Three-point bending of ( ) and vertical compression of
( ) showing Instron testing setup.
(HDPE), selected for its homogeneity and ease of CNC ma-
chining. A three-axis lathe was used to cut profiles from solid
HDPE blocks.
Machined beams were tested on an Instron universal testing
machine using a custom three-point bending fixture. Load was
initially increased at a rate of 500 N/min from 0 to 5000 N, fol-
lowed by 2000 N/min thereafter. The setup is shown in Fig-
ure 6.
Tests began with a traditional IPE100 I-beam profile (also
made of HDPE) as a control, followed by:
•( ): a decorative Google font with oversized
flanges,
•( ): a minimalist, near-rectangular profile,
•( ) and (): tested under verti-
cal compression.
3
Stress-strain data was used to extract the ultimate
strength—the maximum load the beam could sustain before
permanent deformation or failure. This point was used as the
benchmark for beam performance.
2.3. Computational Simulation Pipeline
To expand beyond the handful of beams fabricated physi-
cally, a simulation framework was built in Python and Abaqus.
The method is shown graphically in Figure 7 and described be-
low.
Figure 7: Simplified computational simulation pipeline. Fonts are loaded in
A, cropped to fit into a 1:1 square, and scaled to a 1000 px ×1000 px canvas.
In B, the glyph is converted into a series of points and lines. The red cross
marks an interior point used to define the filled region for both mesh generation
and boundary condition assignment. Green dots represent corners, while blue
lines define edges (lines rather than curves in this example). In C, the profile
is extruded, meshed, boundary conditions applied, loads defined, and results
generated. Colors represent von Mises stress, the primary failure metric.
All installed fonts were scanned, with each capital
letter rendered at high resolution and centered on a
100,000 px ×100,000 px canvas. The glyph was then cropped
and uniformly scaled to fit the canvas bounds. To ensure
machinability, floating segments were connected using at least
one 20 px-wide link.
The modified glyph was then vectorized by converting it into
a series of points and line segments. Although fonts are often
defined as vector graphics, variations in formatting and encod-
ing across typefaces made automated interpretation impractical.
The high pixel resolution preserved edge fidelity in the absence
of reliable pre-defined vectors.
These vector instructions were then passed to an
Abaqus/CAE instance, where they were used to define a 12 cm-
wide cross-section extruded to 500 mm in length—matching
the physical test setup. Simulations initially used HDPE to
validate against lab data, before switching to structural steel
to better reflect real-world applications. Since only relative
performance was of interest, any isotropic, linear-elastic
material would suffice.
Mesh seeding was tested at 5.0, 1.0, 0.5, and 0.1 mm. A
0.5 mm seed produced consistent results with acceptable run-
times (under five minutes per beam).
For the bending tests, one end of the beam was fully con-
strained (pinned in vertical, horizontal, and lateral axes), while
the opposite end was fixed vertically but free to slide laterally.
Rather than point loading, a uniform virtual gravity load was
applied to simulate distributed bending. Each beam experi-
enced a total of 1000 N of force, with the gravity value adjusted
accordingly—for instance, a 4 kg beam was assigned 250 m/s2
gravity, while a 50 kg beam received 20 m/s2.
Additional simulations included:
•Axial compression, with a fixed base and distributed com-
pressive load at the top.
•Tension, with an encastre base and uniform axial tension.
•Torsion, applied via rotational boundary conditions using
a reference point.
Simulations output von Mises stress, principal stresses, and
failure estimates. Although early tests stepped up load until
failure, later analyses used relative stress under fixed loading to
infer failure: under Hookean assumptions, the profile with the
highest stress under identical loading is expected to fail first.
2.4. Validation and Comparison
To confirm simulation fidelity, the best- and worst-
performing profiles from the bending simulations were selected
for CNC fabrication and physical testing. These beams were
tested on the same Instron bending rig. Measured ultimate loads
were compared to simulated predictions, and results were found
to align closely (around 10% deviation), sufficiently validating
the computational pipeline.
3. Results and Discussion
3.1. Bending Performance
Experimental bending data are shown in Figure 8, with a
comparison of physical and computational results presented in
Table 1. Simulation error was typically around 10%, with the
largest discrepancy observed in the ( ) typeface. This
level of error is consistent with expectations in the literature and
is acceptable given the difference in loading methods (cylindri-
cal Instron plate versus distributed body force).
To contextualize performance across the full set of 1,000
typefaces, Figure 9 plots simulated bending strength against
4
Figure 8: Instron stress-strain data for bending under load.
Table 1: Comparison of physical and computational ultimate load under bend-
ing for selected typefaces.
Profile Measured (N) Simulated (N) Difference (%)
IPE100 16,237 14,068 13
( ) 25,800 21,700 16
( ) 20,000 22,100 −11
( ) 18,600 19,500 −5.2
( ) [Zapfino] 1,600 1,730 −8.0
beam mass. Lines passing through the origin represent beams
with equal strength-to-mass ratios. These group glyphs with
functionally identical structural efficiency.
Straight-line fonts trace a diagonal from the origin to the top-
right, where performance increases with beam width. Examples
include , , and the filled square ( ). Fonts
above this line are efficient; those below are structurally subop-
timal. Italicized or asymmetric glyphs often failed early due
to lateral instability, with [Zapfino] performing the worst
among popular fonts. Symmetric glyphs with pronounced
flanges—like —performed well, closely re-
sembling traditional I-beam geometry. Only
surpassed IPE100 in relative performance, improving on the I-
beam by replacing fillets with widened flanges.
With these results in hand, we now extend our analysis to the
rest of the alphabet. Figure A.13 in the Appendix presents these
comparisons.
3.2. Buckling Performance
Experimental buckling results are shown in Figure 10, with
simulations compared in Table 2. Agreement was generally
good. The font exhibited a high percentage error,
but given its low load capacity, minor deviations had amplified
effects. Discrepancies may also result from fabrication defects
or minor misalignments in the test setup.
Under axial compression, the performance of fonts was pri-
marily dictated by their lateral symmetry and width. Straight-
Table 2: Comparison of physical and computational ultimate load under buck-
ling for selected typefaces.
Profile Measured (N) Simulated (N) Difference (%)
( ) 24,300 21,700 −9.0
() 4,290 5,880 −37
line fonts buckled at relatively low loads. In contrast, rounder
and more evenly distributed profiles withstand greater loading.
The most reliable performers in buckling were the O’s and D’s,
whose near-circular or oval geometry resists collapse in all di-
rections. This reinforces the notion that uniform cross-sectional
strength is key to preventing buckling—especially in slender
members.
3.3. Tension
Tension was the most predictable stress mode: performance
scaled linearly with cross-sectional area. Shape played little
role; fonts with thicker strokes consistently outperformed thin-
ner ones regardless of their stylistic flourishes. Figure A.15 in
the Appendix shows that deviations from the expected linear
trend are minor and likely due to meshing resolution or interpo-
lation artifacts within the finite element model.
3.4. Torsion
Torsional performance was dominated by the distribution of
material away from the centerline. Round, symmetric fonts
such as capital O’s, B’s, and D’s resisted twisting most ef-
fectively. This aligns with established principles of polar mo-
ment of inertia, where mass concentrated at greater radial dis-
tance enhances torsional stiffness. Fonts designed with ge-
ometric roundness—like and —consistently
performed well, while those with gaps or disconnected strokes
(such as C’s) suffered early failure due to stress concentrations
and incomplete load paths.
3.5. General Patterns and Font Family Trends
Trends emerged across font classifications. Serif fonts gener-
ally landed mid-range in performance: their decorative features
sometimes introduced inefficiencies, but also often enforced
symmetry. Sans-serifs were more diverse, ranging from struc-
turally sound profiles (e.g., ) to minimal forms
that underperformed. Handwritten and script fonts consistently
performed poorly due to irregular stroke widths, asymmetry,
and lack of structural continuity.
3.6. Accuracy and Result Summary
Simulation results matched theoretical predictions when nor-
malized by the mass moment of inertia, as shown in Figure 11.
Outliers typically featured unexpected internal voids or asym-
metries—features that underscore the value of full-field simu-
lation over purely analytical methods. The highest and low-
est performers across all loading regimes are listed in Table 3.
Rankings were determined based on strength-to-mass ratios,
with rotated characters denoted by subscript.
3.7. Conclusions and Practical Implications
This study reimagines the I-beam not as a fixed standard but
as a typographic possibility space. By exploring over a thou-
sand digital typefaces—each with its own historical, aesthetic,
and geometric rationale—we uncover a landscape of structural
performance shaped by the same visual language that guides
5
Better than a rectangle
Better than IPE100
Worse than a rectangle
IPE100
A1
B
C
A2
BioRhyme
Zapfino
Courier New
Figure 9: Simulated ultimate bending load vs. beam mass. Sloped lines passing through the origin represent constant strength-to-mass ratios. A1 denotes the origin
(rectangle with zero width) and A2 the completely filled-in square. Straight-line fonts fall along the A1–A2 line, separating efficient (above) from inefficient (below)
designs. Only ( ) outperforms the traditional I-beam benchmark.
6
Table 3: Top and bottom performers by stress mode and overall ranking (from best as 1 to worst as n). Rotated characters are indicated by subscript.
Rank Bending Buckling Torsion Overall
Letter Font Letter Font Letter Font Letter Font
1 BioRhyme, I Honk Filled ( ) Erica One Noto Serif, O Monofett Noto Serif, O Erica One
2 IPE100 control Courier New Erica One, D Gasoek One Medieval, O Honk Filled ( ) Gasoek One
3 Azeret Mono, I Cutive Mono Gill Sans, N Gajraj One NATS, O Erica One Archivo, Hrot Gajraj One
n-2 Herbertian, Q Kristi Murecho, I Foldit Murecho, I Foldit Glory, V Informal Roman
n-1 Fuggles, Z Mr Dafoe Big Shoulders, I Dorsa Montserrat, I Amatic SC Genos, Z Fuggles
n Genos, Z Mrs Sheppards Anybody, I Big Shoulders Georama Big Shoulders Kristi, J Kristi
Figure 10: Instron stress-strain data for buckling under load.
human communication. While the traditional I-beam remains
effective, it is not singular.
Glyphs like the of and the rotated H ( ) in
demonstrate that symmetry, flange width, and
distributed mass can be optimized even further. Others, such
as ’s I, achieve better load-bearing ratios than
IPE100 itself. Conversely, stylized scripts and asymmetrical
fonts fail early—highlighting the value of simulation in pre-
screening unlikely candidates. and were
among the most consistently strong across all categories. As
shown in Figure 12 one could imagine a bridge or building
made of an alphabet soup of such fonts.
From a design perspective, this work invites structural engi-
neers to look beyond convention. The alphabet offers a ready-
made testbed for cross-sectional creativity. As additive man-
ufacturing and digital design tools continue to advance, engi-
neers may one day specify load-bearing members not just by
shape, but by font.
Acknowledgements
The authors thank the MIT Hobby Shop for assistance with
beam fabrication and the MIT MakerWorkshop for access to
the Instron testing machine. Special thanks to Julia, Lydia, and
Mary for technical support throughout the project, and to Olivia
and Kyle for graciously offering their dining room table to hold
dozens of in-progress typeface beams.
Appendix A. Supplementary Figures and Tables
Results and code are available at https://github.
com/AtomicFrontierCode/typefaces. For supplementary
Figure 11: Ultimate bending strength vs. theoretical moment of inertia. Fonts
closely tracking the curve perform as expected; outliers reveal inefficiencies
due to geometry which are only examinable during to to finite element analysis
of experimental testing.
Figure 12: Example infrastructure that could be built using beams of
(L) and (R).
figures and experiment videos see: https://youtu.be/
AQJDKs8jsjk.
References
[1] C. J. Merfinger, Bridges through the ages: Part 1. the beginning, The
Military Engineer 53 (353) (1961) 198–203.
URL http://www.jstor.org/stable/44568788
[2] R. A. Jewett, Structural antecedents of the i-beam, 1800–1850, Technol-
ogy and Culture 8 (3) (1967) 346–362.
[3] G. P. Raidabaugh, Origin and Development of Railroad Rail, English and
American, Wood, Iron, and Steel, Self-published, Philadelphia, 1915.
[4] P. B. Meggs, A. W. Purvis, Meggs’ history of graphic design, John Wiley
& Sons, 2016.
[5] R. Bringhurst, R. Bringhurst, R. Bringhurst, The elements of typographic
style v3, Harmony 17 (2008) 25.
[6] N. A. Haefner, Ubiquitous design: A study of popular fonts and typo-
graphic understanding (2020).
7
Figure A.13: Simulated ultimate bending load vs. beam mass for the entire
alphabet. IPE100 is shown the the yellow dot and the good/bad line in green.
Figure A.14: Simulated ultimate buckling load vs. beam mass for the entire
alphabet. IPE100 is shown the the yellow dot and the good/bad line in green.
Figure A.15: Simulated ultimate tension load vs. beam mass for the entire
alphabet. IPE100 is shown the the yellow dot and the good/bad line in green.
Figure A.16: Simulated ultimate torque load vs. beam mass for the entire al-
phabet. IPE100 is shown the the yellow dot and the good/bad line in green.
8
[7] O. Toirov, N. Tursunov, Development of production technology of rolling
stock cast parts, in: E3S Web of Conferences, Vol. 264, EDP Sciences,
2021, p. 05013.
[8] W. L. Roberts, Cold rolling of steel, Routledge, 2017.
[9] C. Bailey, T. Bull, A. Lawrence, The bending of beams and the second
moment of area, The Plymouth Student Scientist 6 (2) (2013) 328–339.
[10] L. Laim, J. P. C. Rodrigues, L. S. da Silva, Experimental and numerical
analysis on the structural behaviour of cold-formed steel beams, Thin-
walled structures 72 (2013) 1–13.
[11] R. Chandra, I. Chopra, Experimental and theoretical analysis of compos-
ite i-beams with elastic couplings, AIAA journal 29 (12) (1991) 2197–
2206.
[12] M. Fr ˘
atit
,a, F. Popescu, K. Uzuneanu, I. Ion, C. Anghelut
,˘
a, About struc-
tural and thermal analysis of diesel engine piston using ansys software,
in: IOP Conference Series: Materials Science and Engineering, Vol. 595,
IOP Publishing, 2019, p. 012041.
9
