Mathcad - LCA (Load Case Algorithm) by Julio C. Banks, PE.xmcd

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Steel Beam Designby Julio C. Banks, PE

Two beams made from 2-2x8 wood with intermediate supports are to be replaced by steel beams support at each end. The shortest beam has one (1) intermediatesupport and the longest beam has two (2) intermediate supports.

The existing loads on the 2-2x8 wood beams are not known and must be estimatedby the PE.

Solution

The method of estimating the existing beam loads is by using the flexural capacityof the wood beams and the self-weight. An FEA software will be used to determinethe maximum live load that the 2x8 wood beam will be able without causingstructural failure of the beam.

ASCE 7-10, Section 2.3.2 - Basic Load Combinations

Load combinations 1 and 2 are the most critical when only D (Dead) and L (Live)clods are to be considered.

1. 1.4D2. 1.2D + 1.6L

One must select the maximum load case with the following procedure:

Determine the D/L ratio (or L/D) at which the maximum load case is determinedautomatically by asking the question "When is Load Case No. 1 Greater than orequal to Load Case No. 2?" i.e., when is LC1 LC2 ? or when is 1.4 D 1.2 D 1.6 L ? Now, solve for a convenient ratio.

1.4 D 1.2 D 1.6 L 1( )

Divide Eq. 1 by 1.2 7

6D D

4

3L 2( )

Divide Eq. 2 by D 7

61

4

3

L

D 3( )

L

D

7

61

3

4

L

D

1

8 or D

L8 4( )

Julio C. Banks, PE

Mathcad - LCA (Load Case Algorithm) by Julio C. Banks, PE.xmcd

page 2 of 3

When equation 4 is satisfied (yes-case) then load case 1 governs.

Equation 4 is now converted into an algorithm that will calculate which load casegoverns and will state the governing load case. Load case No. 1 governs if D/L isgreater than or equal to 8, otherwise, Load case No. 2 governs.

The load U is to be used in in classical calculations by adding the self-weight to thedead load.

LCA D L( ) "LCA (Load Case Algorithm)"

Solution

1

1.4 Dplf

D

L8if

2

1.2 D 1.6 L( )

plf

otherwise

Solutionreturn

5( )

ExampleThe ASCE 7-10 minimum live load for storage is 20 psf. The maximum live load fora given dead load that a 2-2x8 beam could resist without failure and a utilization of0.96 or 96 % is 25 psf. When such a live load of 25 psf was applied to the known tributary results in the distributed live load given in this example

Dead load: D 17.71 plf Live load: L 236.1 plf

D

L0.08

The LCA (Load Case Algorithm) produces both, the governing load case and itsmagnitude.

Load_Case_No LCA D L( )1 2

U LCA D L( )2 plf 399.0 plf

Julio C. Banks, PE

Mathcad - LCA (Load Case Algorithm) by Julio C. Banks, PE.xmcd

page 3 of 3

The following 3-steps procedure produces the governing load case, U, producing thesame results as the algorithm presented in equation 5.

LRFD1.4 D

1.2 D 1.6 L

24.79

399.01

plf

U max LRFD( ) 399.0 plf

Load_Case_No ifD

L8 1 2

2

Julio C. Banks, PE