LRFD Load Combinations

Choose the combination that results in the highest U, use U in your calculations.

$$U = 1.4(D+F)$$

$$U = 1.2(D+F+T) + 1.6(L+H) + 0.5(L_r or S or R)$$

$$ U = 1.2D + 1.6(L_r or S or R) + (1.0L or 0.8W)$$

$$ U = 1.2D + 1.6W + 1.0L + 0.5(L_r or S or R)$$

$$ U = 1.2DL + 1.0E + 1.0L + 0.2S$$

$$U = 0.9D + (1.6W or 1.0E) + 1.6H$$

D = Dead Load, L = Live Load, T = self-straining, H = earth pressure, \(L_r\) = roof live load, S = Snow Load, R = rain load, E = earthquake load

In some sample problems I have seen \(\gamma\) and Q variables. Individual load factors like 1.2 and 1.4 are sometimes represented as \(\gamma\) and the loads themselves are represented as \(Q\). The factoring for a single load would then be \(Q \gamma\), and all of them \(U = \sum{Q \gamma}\).

Strength Reduction Factor (\(\phi\))

Strength reduction factors are applied to the nominal (design) strength:

$$ \phi R_n \geq P_u $$

or (this is seen pretty often in practice)

$$ R_n \geq \frac{P_u}{\phi}$$

Where \( P_u \) is determined with U from the factored loads. Strength reduction factors vary for concrete and steel.


0.9 for Tension controlled

0.7 compression with spiral steel

0.65 compression with tied steel

0.75 shear and torsion

0.65 bearing on concrete

Furthermore there is a range based on stress (\(\varepsilon\)) value for beams (\(0.48 + 83 \varepsilon\)) and the same equation applies to tied transition members. Spiral transition members use \(0.57 + 67 \varepsilon\).


0.9 for yield and 0.75 fracture

About Conrad

I am a Civil Engineer. I work in San Diego and am preparing to take the PE Exam. I am interested in surfing, business, travelling, and spending time with my wife. Thanks!

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