Capacity Curve
Certainly these resisting capacity will be different for each building.
Resisting capacity of an existing building can be defined by capacity curve. See the following figure.
Image snipped from a document : here
Here in Y-axis is lateral force and in X-axis is lateral deformation. So up to the elastic range (yield point) deformation will increase with the increasing force. For additional force after reaching the yield point the curve typically decreases slightly because of dislocations of material. As deformation continues, the stress increases on account of strain hardening until it reaches the ultimate strength.
During this deformation process, building experience the slight , moderate , extensive and complete damage state with the increasing amount of lateral force.
From above we can tell that for a certain lateral deformation building will slightly damage. Let the deformation amount is 0.90 inch . If the deformation continues with the load it will be in moderate damage state. Let for moderate damage state deformation is 1.5 inch. Similarly for extensive damage deformation is 1.8 inch and for complete damage lateral deformation is 2.5 inch. So the damage state of a building depends on the lateral deformation.
Now, to better understand the existing building behavior during a certain earthquake load we need to construct the capacity curve of that building. We can do the pushover analysis to construct such curve of that building. But for constructing capacity curve of an existing building we need to model that building first. For modeling we need to know the architectural as build drawing , compressive strength of existing column, beam, reinforcement detailing of beam column, slab detailing and all other vulnerable factors presented on that building.
For representing a capacity curve in Hazus we need to mention yield point (Dy,Ay), ultimate point (Du,Au), and other parameters like kappa, damping fraction etc. of that capacity curve.
**Hazus does not need this graphical curve , it needs the representing value of the curve so that it can make a equation of that curve. As it is easier to make calculation with the equation.
Remember, In Hazus we are dealing with thousands of buildings. So practically it is not possible to model each building and find out the respective capacity curve. So we need to categorize the the buildings according to their structural type like there may be concrete building, masonry building , steel building etc.
For detail category of building types see Inventory Collection section.
There are 36 structural types in Hazus. So for Hazus analysis we need to construct these 36 types of capacity curves if 36 types of buildings are available in our study area.
For an example we want to derive capacity curve for C3L building. In Hazus there will be only one capacity curve for all C3L type buildings.
C3L= Beam, column with masonry walls low rise buildings (1 to 3 stories)
We know the capacity curve of 1 storey building will be different than that of 2 storey building or 3 storey building. Again if there presents any vulnerable factors in the building , capacity curve will be different than that of the same height building which do not have any vulnerable factors. For better understanding see the following figures.
For detail category of building types see Inventory Collection section.
There are 36 structural types in Hazus. So for Hazus analysis we need to construct these 36 types of capacity curves if 36 types of buildings are available in our study area.
For an example we want to derive capacity curve for C3L building. In Hazus there will be only one capacity curve for all C3L type buildings.
C3L= Beam, column with masonry walls low rise buildings (1 to 3 stories)
We know the capacity curve of 1 storey building will be different than that of 2 storey building or 3 storey building. Again if there presents any vulnerable factors in the building , capacity curve will be different than that of the same height building which do not have any vulnerable factors. For better understanding see the following figures.
Fig 1: C3L buildings of different storey height.
All of the buildings shown above are C3L but resistance capacity of earthquake will be different.
Fig 2: 2 and 3 storey C3L buildings with soft storey
Resistance capacity of C3L building in Fig 2 will be different than that of Fig 1 because there presents a vulnerability factor (Soft Story).
Fig 3: C3L buildings with soft storey and heavy overhang.
Resistance capacity of C3L buildings in Fig 3 will be different than that of in Fig 1 and Fig 2 because there presents 2 vulnerable factors (Soft storey & heavy overhang) though all of them are C3L buildings.
Though all of the buildings in Fig 1 , Fig 2 & Fig 3 are C3L, capacity curve will be different for each building. Here I have shown 3 possibilities but there may be other possibilities like C3L with short column, C3L with short column and heavy overhang etc.
We need to model each combination possibility available in our study region and find out the capacity curve. Here in our study 10 C3L buildings are modeled (some model names are given in the above figures). Model parameters are like below.
