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Tributary area(Loading)

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Let consider a slab supported by beams and columns, to begin structural analysis for each member, we need to know the amount of load transferred to this member, the amount of load transferred to any member can be determined using tributary area(loading) concept. the geometry of a structure will determine the shape of the tributary area.


In a one-way system, slab delivers the load to supports by one-way action. the dimension of slab shall satisfy the following equation to act as one-way slab L2/L1>2. let consider floor system in figure 3, L2/L1 for beam AB L2/L1=15/5=3, therefore slab will transfer the loads to beam in one-way action, tributary area for beam AB, E-f will be as shown in figure 3, loads of 100*2.5=250Lb/ft(linearly distributed over the whole length of the beam, for beam CD, the load will be 100*5=500Lb/ft, beam CD will share loads from both sides because it is located at the center of slab. beams AB, CD, EF will transmit the loads to girder AE and BF, girder AE, and BF will share the half of load for each beam as shown in figure 4. 

Figure 2
Figure 3



Figure 4

Now let consider reinforced concrete slab in figure 5, this slab supported by four edge beam AB, BD, DC and CA, L2/L1=10/10=1, therefore, it is a two-way slab, for the two-way slab the distribution of load for beam AB will be as shown in figure 5, diagonal at 45 angle will be drawn from point A and point B, the tributary area will be triangle, in this example the tributary areas area equal for all beams because L1 and L2 are equal, the distributed over beam AB will be a triangle shape similar to tributary area, this load will be zero at point A and B, then increasing to maximum value equal to 5*100=500Lb/ft as shown in figure 5




Figure 5


if we consider slab in figure 6, L2/L1=1.5 so it is a two-way slab, a diagonal line at 45 angle will be drawn for beam AB from point A and B, because the length and width of the slab are not the same, the tributary area for beam AB will be trapezoidal as shown in figure 6. the load distribution over beam AB will be similar to tributary area with peak load equal to 5*100=500 Lb/ft.
Figure 6


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My name is Mohammad Hamdan, and I am a Civil/bridge Engineer with extensive professional background and experience in the field of construction. I have 10+ years of experience in the construction field. During my professional career, my emphasis has been placed on structural projects, mainly bridges, infrastructure and roads. Reading and practicing the design of structures is my passion.i was lucky to be a part of a big team that executed major highway interchanges. I believe in spreading the knowledge, thus, i compose these courses to share my experience and knowledge. My course focuses on the practical side of construction field. On other word, i am sharing some of what new engineers need to know about construction field. Beside working on construction field, i love writing some articles on my website ( curious civil engineer) Moreover, i wrote some engineering papers, you can check them  by searching my name on Google (Mohammad mamon Hamdan)