LRFD vs ASD in steel design, with a worked PEB example

Two ways to apply one safety margin

Every steel design check comes down to the same comparison: is what the structure can carry larger than what we ask it to carry, with a margin? AISC 360 lets you express that margin in two ways.

• LRFD, Load and Resistance Factor Design: φR_n ≥ R_u. The required strength R_u comes from loads multiplied by load factors (1.2 for dead, 1.6 for live, and so on). The nominal strength R_n is reduced by a resistance factor φ (0.90 for flexure and compression in most cases).
• ASD, Allowable Strength Design: R_n/Ω ≥ R_a. The required strength R_a comes from loads combined at service level, and the nominal strength is divided by a safety factor Ω (1.67 for flexure and compression in most cases).

The important thing, and the thing people forget, is that R_n is the same in both. Since the 2005 edition, AISC 360 has used one set of nominal strength equations for both methods, with Ω calibrated so that Ω ≈ 1.5/φ. The only real difference is how the safety margin is split between the load side and the resistance side.

The load combinations side by side

The combinations come from ASCE 7 (or the governing building code). For a typical PEB roof with dead load D, roof live load L_r and wind W, the ones that usually matter are:

Simplified for a roof with no floor live load, snow, crane or seismic effects. Use the full set from your governing standard.

Notice the wind factors. Since ASCE 7-10, wind loads are given at strength level, so LRFD uses 1.0W and ASD scales it to 0.6W. If you are working from older references that show 1.6W in LRFD, they predate that change.

A worked example on a PEB rafter

Let’s take a rafter section near the haunch and suppose the analysis gives these unfactored bending moments from each load case. The numbers are illustrative only, chosen to make the arithmetic easy to follow, not taken from a real building:

• Dead load D: 40 kN·m (sagging sense taken as positive)
• Roof live load L_r: 30 kN·m
• Wind W (uplift): −70 kN·m

LRFD

• 1.4D = 1.4 × 40 = 56 kN·m
• 1.2D + 1.6L_r = 48 + 48 = 96 kN·m (governs gravity)
• 0.9D + 1.0W = 36 − 70 = −34 kN·m (governs reversal)

Required nominal strength for gravity: M_n ≥ 96 / 0.90 = 106.7 kN·m.
For uplift: M_n ≥ 34 / 0.90 = 37.8 kN·m in the opposite sense.

ASD

• D + L_r = 40 + 30 = 70 kN·m (governs gravity)
• 0.6D + 0.6W = 24 − 42 = −18 kN·m (governs reversal)

Required nominal strength for gravity: M_n ≥ 70 × 1.67 = 116.9 kN·m.
For uplift: M_n ≥ 18 × 1.67 = 30.1 kN·m.

What the example tells us

For gravity, ASD asks for about 10% more nominal strength than LRFD here. For uplift, ASD asks for about 20% less. Which one sets the section depends on which check governs the member. For the inner flange near the haunch, gravity usually governs; for the outer flange and the unbraced bottom flange under uplift, the reversal case often does. The two methods can therefore push different members up, which is why the optimised sections are rarely identical.

One more caution: under reversal the compression flange changes, so the lateral-torsional buckling check uses a different unbraced length. The capacity in each direction is different, and the comparison above only compares the required strengths.

Where the two methods cross over

For a dead plus live combination you can find the ratio at which LRFD and ASD demand the same nominal strength. Setting (1.2D + 1.6L)/0.90 equal to 1.67(D + L) gives L/D ≈ 3.1.

• Below that ratio (dead-heavy structures), LRFD needs less nominal strength.
• Above it (live-heavy structures), ASD needs less.

PEB roofs are light, so roof live load can be a large multiple of the sheeting and purlin dead load once you exclude collateral. That puts many PEB rafters closer to the crossover than heavier buildings, which is one reason the LRFD versus ASD choice tends to matter less for PEB than people expect.

Mistakes we see in LRFD and ASD checks

Most errors in practice have nothing to do with which method is better. They come from mixing pieces of the two, or from carrying old habits forward. These are the ones we catch most often when reviewing PEB designs:

• Old wind factors. Using 1.6W in LRFD or 1.0W in ASD with wind pressures from a current edition of ASCE 7, which already gives strength-level wind. The result is a frame designed for far more wind than intended, or far less.
• Mixing the two methods. Taking LRFD forces from one set of combinations and checking them against allowable (ASD) strengths, or the other way round. The safety margin is either applied twice or not at all.
• Missing the reversal case. Leaving out 0.9D + 1.0W (LRFD) or 0.6D + 0.6W (ASD). On light PEB roofs this is often the case that governs the rafter bottom flange and the column outer flange.
• Serviceability on factored loads. Deflection and drift are checked under service loads in both methods. Using LRFD combinations for deflection makes the frame look far more flexible than it is and pushes sections up for no reason.
• Assuming one method is always lighter. As the worked example shows, LRFD and ASD can each govern different members of the same frame. The only reliable comparison is to design the whole frame both ways.

If your office designs to IS 800 as well, note that its partial safety factors on loads (Table 4) play the same role as LRFD load factors, so the same discipline applies: one consistent set of combinations for strength and a separate one for serviceability.

Choosing between LRFD and ASD

In practice the choice is often made for you: the client, the PEB supplier’s standard, or the checking authority specifies it. When it is open, we look at three things:

1. Consistency with the rest of the project. Foundations, connections and secondary members should follow the same method.
2. The load mix. Heavy collateral or equipment loads lean towards LRFD; light roofs dominated by live or wind are close to neutral.
3. Team familiarity. Many engineers trained on allowable stress find ASD more intuitive; LRFD aligns better with IS 800’s limit state approach for offices that use both codes (see IS 800 vs AISC 360).

If you want a number rather than an opinion, optimise the frame both ways. The PEB Optimization Tool reads the method from your STAAD.Pro model and searches tapered built-up sections against AISC 360 in LRFD or ASD (or IS 800:2007), keeping the lightest section that passes. Running it twice and comparing the frame weights takes minutes rather than a day of manual iterations. To see how a tapered member is proportioned in the first place, read designing tapered built-up I-sections.