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Section 2.4.1
Example Problem 2.1
Last Revised: 11/04/2014
Given: The beam shown in Figure 2.4.1.1 supports a floor system and a column. It also acts as a drag strut in the lateral load resisting system of the building that it is a part of. The load sources are:
- Source 1: Floor loads (acting as a uniform load over the entire span). This load consists of 1.15 k/ft dead load and 1.85 k/ft live load.
- Source 2: Column loads located a distance "x" from one end of the beam. This is a point load source. The column load consists of 8.00 k dead load, 4.80 k live load, and 10.0 k snow load.
- Source 3: An axial force that consists of 15.0 k wind load or 25 k earthquake load.
Figure 2.4.1.1
Example Problem 2.1 Beam Load Diagram
Wanted: Draw the beam load diagrams for LRFD LC2b and LRFD LC5b. (Note that these two load combinations are chosen for example purposes only. This exercise can be done for ALL of the load combination equations and their permutations.)
Solution: Click on this link to see the detail of the problem statement, the given data, and a hand solution for developing a load diagram for the two different LRFD load combinations.
The problem statement describes three different sources of load applied to the beam. The first is a uniform load that goes the length of the beam. The second is a point load that is a column reaction. The third is an axial force induced in the member by wind and earthquake forces applied elsewhere on the structure.
While the beam must be capable of supporting all the load combinations, we will limit the solution in this hand solved example to only two combinations. Hopefully this will be sufficient for you grasp the basic concept.
You will notice that the 2nd LRFD load combination can have three permutations. To simplify the problem at this point we only consider the permutation that includes snow load, LC2b. You will observe how the same load combination is applied to each load source and its contributing forces. The result is the load diagram shown.
The second load combination considered is LRFD LC5 which has two permutations. We are only going to consider one, LC5b. See how the equation is applied to all sources resulting in the load diagram shown.
Comparing the results, which one would be the controlling case? You might be tempted to say LRFD LC2b because the point and uniform loads are greater than in LRFD LC5b. To the trained eye, that might not be the case. The presence of the axial compression force in LRFD LC5b might just cause it to control the design depending on what member is selected. If these were the only two load cases to be considered, you should check your beam design to make sure it satisfies BOTH load combinations.