# 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.

### Concrete

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 \(0.57 + 67 \varepsilon\).

### Steel

0.9 for yield and 0.75 fracture

Posted in Structural Breadth and tagged asd, dead load, live load, lrfd, strength reduction factor, structural. Bookmark the permalink. Leave a Comment.

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