# Structural Engineering Rules of Thumb

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Before the advent of computers and advanced computational abilities, engineers were capable of building much of the world’s existing infrastructure. To do this, they did not necessarily spend staggering amounts of time to grind through calculations by hand. Instead, other mathematical methods were developed to quickly, and with a reasonable amount of accuracy, shortcut the process.

Previous generations of engineers known for mastering their craft functioned with “rules of thumb” and with old habits that were proven reliable through simple experience.  Trial and error in the “real” world facilitated an instinctive knowledge of structures.  Engineers used hand calculations which involved running linear regression analyses. These derived special ratios and constants that simplified common design computations.  This allowed the engineer to determine required materials and dimension on site with a simple bit of division and multiplication.

These approximations became unnecessary once computer assisted design (CAD) and building information modeling (BIM) started leading the industry in an age of computers. Consequently, many of these shortcuts and estimation tactics are being lost and forgotten.  Their usefulness, however, remains.  Though the calculations happen behind computer software, some required input values still need hand-figured solutions.  Also, much time may be saved if initial values are reasonably close to begin with.  Structural engineers often find how valuable these “outdated” techniques become when an on-site and/or rapid design decision is required.  The irreplaceability of rule-of-thumb methods, however, is most evident in simple “reality checks.”  No matter how reliable software may be, common sense and practical intuition must be used to check the validity of results.  Even if a machine is infallible, the human running it may make a modeling error.  Using simple math to verify can catch large mistakes that would have been over-looked otherwise, and prevent errors that would cost heavily in time and resources.

Listed below are several of these rule of thumb techniques compiled and notably presented by Socrates A. Ioannides, Ph. D., S.E. of Structural Affiliates International. (See "Rules of Thumb for Steel Design" link below).

For a steel beam of cross-sectional area A in square inches and a weight of Wt in pounds per foot:

A = Wt/3.4

Where A is the cross-sectional area of a steel beam and Wt is the weight of the steel shape.  This formula is derived using the density of steel.

For a steel I-beam of height d

Ix ≈ d2 * Wt/20

This formula uses the previous area rule of thumb to approximate the moment of inertia for a steel I-beam.

Plugging this into the equation for section modulus we get:

Sx ≈ d * Wt/10

Through graphical observation we can find a relationship between radius of gyration and the height and width of the cross-section:

rx ≈ 45% * d

ry ≈ 25% * b

Substituting the previous assumption for section modulus into the formula M=Fb * Sx we get:

Wt ≈ 5 * M/d for an allowable 24 ksi bending stress and

Wt ≈ 3.5 * M/d for an allowable 50 ksi bending stress and

70% to 75% of the moment is used in these formulas for composite beams

Where M is in ft * kips.

Also for three-quarter inch shear connector studs:

Use 1.1 * Wt shear connectors for ASD and

1.25 * Wt shear connectors for LRFD

For trusses:

Achord = 0.61 * M/D

Pchord = 13.33 * M/D

Wtchord 2.06 * M/D

Wttruss ≈ 3.0 Wtchord; Derived from observation

Wt ≈ 6 * M/D

Wt ≈ 4.5 * M/D (for 50 ksi)

For Columns:

Pa ≈ A * (22 – 0.10 * K * L/r) (for 36 ksi)

Pa ≈ A * (30-0.15 * K * L/r) (for 50 ksi)

### Span and depth of structure:

• Roof beam and roof joists: 0.5  *  length = span (ft) and depth (in)
• Floor beams and floor joists: 0.6  *  length = span (ft) and depth (in)
• Composite beams: 0.55  *  length = span (ft) and depth (in)
• Beam Depth = ½ inch per foot of span

### Roof Systems

For cantilever/continuous roof systems:

Hinge or splice location is 15% to 25% times span length

For cantilever/continuous roof beams:

Beams run in the short direction.

Optimum bay size is 30’ x 40’.

For truss joist and joist roof system:

Girders run in long direction.

Optimum bay size is 40’ x 40’.

### Aspect Ratios

The ratio of a building’s height divided by its width is known as its aspect ratio

Typical aspect ratios range from four to nine.

Efficient systems will have ratios less than five.

The different load resisting systems used in structures is dependent on the number of stories included in the building.

29 stories or less = Rigid frame

30 to 40 stories = Frame – shear truss

41 to 60 stories = Belt truss

61 to 80 stories = Framed tube

81 to 100 stories = Truss – tube w/ interior columns

101 to 110 stories = Bundled tube