Chapter X - Formulas and Equations

LOAD AND RESISTANCE FACTOR DESIGN

Nomenclature

D dead loads kips or kips/ft

E earthquake load kips or kips/ft

H load due to lateral pressure kips/ft2

L live loads due to occupancy kips or kips/ft

Lr roof live load kips or kips/ft

Q load effect produced by service load kips

R load due to rainwater or ice kips or kips/ft

Rn nominal strength

S snow load kips or kips/ft

U required strength to resist

factored loads

W wind load kips or kips/ft

Symbols

load factor

resistance factor

 

Required Strength

The required ultimate strength of a member consists of the most critical combination of factored loads applied to the member. Factored loads consist of working, or service, loads multiplied by the appropriate load factors. In accordance with LRFD1 Sec. B2, load combinations shall be as stipulated by the applicable building code. The required strength å Q is defined by seven combinations in IBC Sec. 1605.2.1 as;

∗ Replace 0.5L with 1.0L for garages, places of public assembly, and areas where L > 100 lbf/ft2 .

∗∗ Replace 0.2S with 0.7S for roof configurations that do not shed snow

The following illustration shows how to calculate the loads on a typical a six-story frame building. The loading on the frame is calculated as follows.

roof dead load, including cladding and columns, wDr = 1.2 kips/ft

roof live load, wLr = 0.4 kip/ft

floor dead load, including cladding and columns, wD = 1.6 kips/ft

floor live load, wL = 1.25 kips/ft

horizontal wind pressure, ph = 1.0 kip/ft

vertical wind pressure, pv = 0.5 kip/ft

Determining the maximum/minimum design loads on columns.

The axial load on one column attributed to dead load is

The axial load on one column attributed to roof live load is

The axial load on one column attributed to floor live load is

The axial load on one column from horizontal wind pressure is

The axial load on one column from vertical wind pressure is

From IBC Eq. (16-2), the maximum design load on a column is

Alternatively, from IBC Eq. (16-4),

From IBC Eq. (16-6), the minimum design load on a column is