D-L Governing Load Combination Case Selector Algorithm.mcdx Page 1 of 2

Dead Load and Live Load Combination Selection Algorithmby Julio C. Banks, MSME, P.E., CGC

Reference

ASCE 7-10, ''Minimum Design Loads for Buildings and Other Structures'', Pp. 7 through 9.

Section 2.3.2 Basic Combinations [1] provides seven (7) load cases. The first two (2) loads cases have the largest load factors and therefore will be utilized in this report to pre-select which case governs based on the D/L-ratio (Dead-Live load ratio) based upon a derived algorithm.

Determine the governing load combination when considering Dead (D) and Live (L) load conditions from the following two (2) cases:

1. ＝Pu ⋅1.4 D

2. ＝Pu +⋅1.2 D ⋅1.6 L

Determine the D-L ratio which would cause LC (Load Combination) 1 to govern since it is the simples of the two LCs

Let ＝Λ ―D

L((1))

The method of determining when LC 1 governs is by asking the simple question:When is ?≥⋅1.4 D +⋅1.2 D ⋅1.6 L

≥⋅1.4 D +⋅1.2 D ⋅1.6 L ((2))

Divide Eq. 2 by L in order for the parameter defined by Eq. 1 to be defined in terms of expression 2

≥⋅1.4 Λ +⋅1.2 Λ 1.6

≥⋅0.2 Λ 1.6

≥Λ 8 ((3))

Equation 3 is the answer to the question represented by expression 2; that is, load combination 1 governs whenever the D-L ratio given by Eq. 1 equals or exceeds the factor 8.

Julio C. Banks, MSME, PE, CGC

D-L Governing Load Combination Case Selector Algorithm.mcdx Page 2 of 2

Based upon the D-L Ratio Criterion given by expression 8, one can now proceed to creating an algorithm that would calculate the applicable governing equation of from load combinations 1 and 2.

＝Pu‖‖‖‖‖‖‖‖‖‖

“Force (either point or distributed)”

←Λ ――PD

PL

if

else

≥Λ 8‖‖ ⋅1.4 PD

‖‖ +⋅1.2 PD ⋅1.6 PL

Similarly, the ultimate shear and moment shall be

＝Vu‖‖‖‖‖‖‖‖‖‖

“Shear Force”

←Λ ――VD

VL

if

else

≥Λ 8‖‖ ⋅1.4 VD

‖‖ +⋅1.2 VD ⋅1.6 VL

＝Mu‖‖‖‖‖‖‖‖‖‖

“Moment”

←Λ ――MD

ML

if

else

≥Λ 8‖‖ ⋅1.4 MD

‖‖ +⋅1.2 MD ⋅1.6 ML

Julio C. Banks, MSME, PE, CGC