Hello everyone, welcome to this STATPRO Coffee Corner and today we will see how to use nonlinear pushover analysis in STATPRO. Okay, so this session will be consisting of three parts, so we will start from learning the theoretical background that lies... Beneath the push-over analysis in StarPro implementation. So the push-over analysis is a performance-based analysis and it refers to a methodology in which structural criteria are expressed in terms of achieving a performance objective.
And the performance level describes limiting damage condition which may be considered satisfactory for a given building and given ground motion or excitation. The limiting condition is described by physical damage within the building to the threat to life safety of the building occupants created by the damage and post earthquake serviceability of the building. And the basic approach is to improve the probable seismic performance of the building or to reduce or minimize the existing risks to some certain level.
The performance objective is to obtain desired level of seismic performance of the building which generally is described by specifying maximum allowable or acceptable structural or non-structural damage. Okay, so the objective of the capacity spectrum method, so there are In previous slides, so there are two methods that are used by Puff-Schauer analysis. So the capacity spectrum method and the displacement coefficient method.
So the later one, the displacement coefficient method is utilized in STATPRO. Briefly speaking about the capacity spectrum method, which is objective, so to develop appropriate demand and capacity spectra for the structure and to determine their intersection point. So during this process the performance of each structural component is evaluated.
So we're establishing the demand spectrum and using the techniques described in the code we search for the performance point. So the displacement coefficient method which is used in StatPro, which we will use in our application, is as follows. So we look for the target displacement, delta t, so that is our main goal with this method.
And I would recommend to refer to FEMA 356-2000 year revision, section 3.3. 0.3, 0.3, 0.2 for detailed description of calculation of this target displacement. And according to ATC40 standard force controlled graph refers to components, elements, actions or systems which are not permitted to exceed their elastic limits.
This category of elements are generally referred to as brittle or non-ductile. We see that on the graph type 3, which is brittle force controlled. These type of elements experience significant degradation after only limited post-heel deformation. And on the other hand, the deformation controlled refers to components elements, actions or systems that can and are permitted to exceed their elastic limit in a ductile manner. So we see the curve type 1, ductile deformation control, and force or stress levels for these components are of lesser importance than the amount of deformation beyond the yield point.
We will consider both geometric and material nonlinearities in this static nonlinear pushover analysis in StatProm. And on the right side of the slide we see here a diagram that represents both component actions which are ductile. So the hinge formation for bending moment about local z-axis of a beam.
For force controlled action the curve type III as we had it on the slide before. should be followed and please refer to table C2-1 of FVMA 356-2000 code. So there are examples of possible deformation controlled and force controlled actions.
So major horizontal or vertical portions of the buildings, structural systems that act to resist lateral forces or support vertical gravity loads such as frames, shear walls, frame walls, diagrams and foundations are elements. There are primary elements and secondary elements. STAD will consider primary elements. We will see why a little bit later. So the lateral load distribution is as per section 3.3.3.2.3 of FEMA 356 code chapter 3. So briefly speaking about the lateral load distribution methods so if we can simplify the picture so the first method is uniform distribution of the lateral loads so this is method one and the second method is based on the fundamental mode shape of the building in the direction of the load action.
So in other words it's called inverse triangle distribution. And the third method of the load distribution is the vertical distribution which is consistent of the lateral forces that calculated as a proportion of the total mass at each level. So let's have a closer look at pushover analysis in STATPRO itself.
So in STATPRO the basis for this analysis is the information published in the documents named FVMA 356-2000 and ATC-40. Please note that A license for advanced analysis module is required to use this feature. And according to FEMA 356, steel moment frames are voice frames that develop their seismic resistance through bending of steel beams and columns and moment-resistant beam column connections.
Steel brace frames are those frames that will develop their seismic resistance primarily through actual forces in the components. And user will need to specify whether the structure is a moment frame or braced frame. The first step in this workflow will be to define still moment and braced frames. By default, the program will consider the frame as moment frame.
And currently, Only fully restrained moment frame and concentric braced frame methods are considered. The second step would be to provide the gravity loading information. Those loads are including dead loads and probably live loads.
So dead loads can be taken as calculated structure self-weight without load factors, realistic estimated realistically estimated floor loadings, ceiling, partitions and some other structural or non-structural components and the live loads may be presented as some pre-evaluated values so the consideration should be given to current and expected future. occupancies of this building. The first step would be to mathematically model directly and incorporating the nonlinear load deformation characteristics of individual components and elements of the building, so those elements that will be subjected to monotonically increasing lateral loads representing inertia forces in the earthquake until the target displacement is exceeded. So static nonlinear push-over analysis usually requires multiple analysis cases. And the first push-over load case is gravity load applied to the structure and the rest ones.
So the rest of the load cases may apply different lateral loads in terms of push load increments and whatever the case may be. Then the elements and components that provide the capacity of a structure to resist collapse under seismic forces induced by ground motion in any direction shall be classified as primary, so step number 4, and other elements and components shall be classified as secondary. In a typical building almost all elements including many non-structural components will contribute to the building's overall stiffening, mass and damping, and its response to the earthquake ground motion.
But not all of these elements will have an ability of load carrying capacity or resisting collapse in the ground motion. So the secondary destination will be used when Component or element does not contribute significantly to reliability or resisting to air-off-quake effects. And currently all elements are considered as primary elements in StatRaw. Step number 5 would be to define pushover hinges. So, At the beginning of the analysis, the user will define hinge properties and acceptance criteria for pushover hinges.
And the program includes several built-in default hinge properties that are based on FCMA356, refer to Table 5-6 of FCMA356 and Table 5-7 of the same code for steel structures. And note that while generating inbuilt hinge properties in start following components are considered. So column panel zones considered, fully restrained moment connections considered, partially restrained moment connections considered, steel plate shear walls and elastically braced frames.
And also if any member has releases. So therefore. in member nonlinear stiffness is considered to be the same as it is done for linear member stiffness. The performance of structure and its components is defined by acceptance criteria to provide the desirable information for evaluation of the response and it refers to the specific limiting values of for deformations, loadings, for deformation controlled and force controlled components respectively, which constitute for acceptance seismic performance.
So, there are three criteria. Immediate occupancy, so we'll see that in the model later, term I-O, so this is when the post-surfact structural damage is very limited and the basic vertical lateral force resistance systems of building retain nearly intact like in their pre-earthquake state and so the risk of life-threatening injury from the structural failure is negligible. The second state criteria is life safety abbreviation LS.
and so the post earthquake damage state in which significant damage to the structure may have occurred but some margin against either total or partial structural collapse still remains and the third criteria is collapse prevention abbreviation CP so in this stage the post earthquake structural damage state of the system is on the verge of experiencing partial or total collapse and so right now the program considers only moment hinge for beam and column for steel structures. So if user doesn't define hinge properties, the program will consider built-in default hinge properties based on FVMA. So the step number six would be to perform the pushover analysis and it will be continued until the possible three conditions will be satisfied. So the first one is the cumulative base share will be less or equal to a base share defined by the user. So this is in the case of force controlled.
way, so the user will need to define the base share and until which pushover will be performed since design base share exclude nonlinear effect and when the structure will be subjected to strong earthquake, so the actual base share may be very high compared to the design base share and under this condition there is no guarantee that the structure will Maintain desired performance level. So this option is chosen when the magnitude of base share is known and the structure will be able to support that load. The second condition is displacement at the control joint in the specified direction which will be exceeding the specified displacement.
So this option will be chosen when the amount of displacement is known. So we know how far the structure will move but the amount of base share is unknown and the third option would be so when the structure becomes unstable so the analysis will stop when the structure will become unstable and during analysis instability will rise due to collapse of our different members so make Structions table. And finally, the demand spectrum is generated according to the method described in section 1.6.1.5 of FMA 356. So the program will generate the demand spectrum for the purpose of finding the target displacement and performance check will be done by displacement coefficient method.
Okay, so for each load increment, member sectional forces are checked with the section capacity in order to check formation of the hinge. If sectional force exceeds sectional capacity, hinge formation begins and so this implies member lies on or beyond point B on the low deformation curve we see on the right side and the point B in the low deformation curve denotes the yield point of the hinge and the hinge is assumed to be rigid between points A and B until the yielding starts. And when the hinge reaches the deformation denoted by point C on the graph, it begins to lose the load carrying capacity.
And when it reaches the deformation point E, so the hinge loses all of the load carrying capacity. So, each member scanned along the length of 13 sections for MZ and MY moments, and the maximum moment is located and checked with the section capacity, and if the sectional force exceeds section capacity, the material starts yielding at a particular location, and the hinge at this particular location position is point B. And if bending moment diagram is like figure 1.8, so this happens at initial stage of load increment when the push load is much lower comparing to the dead load, so the chance of forming moment hinge is at two ends and at the span of the member. If bending moment diagram is like on the figure 1.9, so this happens when the push load is much higher than the dead load, and the chance of forming moment hinge is only at sections at or near to the ends of the member.
And when the hinge unloads, the program must find a way to remove the load from the hinge, that was carrying and redistributed to the rest of the structure. And the hinge unloading occurs whenever force deformation or moment rotation curve shows a drop in capacity from point C to point D and the hinge unloads elastically without any plastic deformation. And when the hinge reaches the point C, entire structure is unloaded.
So the program reverses the load on the whole structure until the hinge is unloaded up till the point D. And when hinge reaches the point D, the load is again reversed. So we will see that in our live example how that looks like. So the other structural members will take the load that was removed from the unloading hinge. Okay, so FMA recognizes only three types of frames.
I've mentioned that the two types of frames will be dealt with. So that's the concentric brace frame and moment frame. So user can specify the effective length factor for any member. By default the factors are one in both directions. User can specify if the non-linearity effect will be considered and for convergence check User can specify the both inputs we see here on the screen and these inputs are optional, not necessary to specify, but if you need to run additional convergence checks, so we can do that.
Okay, if command DIST TOL N1 used, so N1 should be the convergence displacement tolerance for convergence of geometric non-linearity and the default value is the maximum span of a structure divided by 120. So this is the default value and the same value as used in non-linear analysis type in StatPRO. And if the user uses the command geocycle n1 where the n1 is number of iterations to be performed for convergence of geometric nonlinearity and default is 1. So if the number of nonlinear iterations exceeds the GeoCycle limit, the analysis will be stopped. Whenever there is a load increment on the structure, so the New analysis cycle starts. and user can specify the maximum number of analysis cycles and note that the load number of cycles specified by user together with number of analysis cycles required in load increment stage plus number of cycles required in linear stage including the analysis cycle for gravity loading limited to 10,001 cycle. Okay, so only the final state is saved for nonlinear static analysis and one may ask to print analysis results of joint displacements, membrane forces and support reactions for the final state of nonlinear static analysis.
and that will be printed in the output file, so you need to specify the print result command. One can ask to print either joint displacements or membrane forces or support tractions. So the command would be print result output and So if you will specify the option 1, so that will be joint displacement, 2, membrane forces, and 3, support reactions.
Okay, so the pattern of the push-load distribution on the nodes of the structure to be entered here, and two types of loading are accepted in push-over analysis, and If one decides to enter the loading pattern manually, so the user-defined incremental push load must be applied only in global X or Z directions. The combinations of X and Z directions are not accepted. And also, the lateral load in those global X and Z directions needs to be applied in the form of joint loads and if the Parameter loading pattern is Loading pattern is zero. So this means that Statpro will internally calculate the lateral push load. So that's the automatic procedure Okay, and for all analysis at least two vertical distributions of lateral load shall be applied and one pattern shall be selected from each of the following two groups, so the group 1 and group 2. Okay, and so therefore two different input files are to be generated and one analysis is to be performed by selecting any one method from group 1 and the second.
analysis, separate analysis should be performed by selecting method 3 from group 2. So the control parameters total base share to be distributed is the optional parameter and it can be used to define the base share that will be distributed vertically along the height of the structure at each floor level. So if base share to be distributed is not defined, so the program will calculate and distribute 10% of gravity loading as lateral load. So by this command, by command LDSTEP, user can specify number of steps for the push load. The default is 100 and lateral load at each floor divided by the number of load steps gives the push load increment at that floor level. One of the two following methods must be specified to define the limit of the pushover analysis.
So actually two of them can be specified in the same input file and whichever exceeding first the limit so the analysis will stop So the first one is pushover analysis will continue until the cumulative base share is less than or equal to base share specified by this command push up to define base share. And the second one is pushover analysis continues until displacement at specified joint at the specified direction exceeds the specified displacement. So that's the option push up to define displacement.
control joint. If the automatic hinge calculation per FMA 356 is not used, then the hinge properties must be defined and these hinges must be assigned to the members. Several hinge properties may be specified with a specific identifier.
and user may later refer this type while assigning specific hinge properties to the members. And if hinge property is not specified, so STAD assumes the FVMA specification will be used. The parameters of this section are used to construct the response spectrum according to FVMA 356. 2000 and the values of spectral acceleration and short period and spectral acceleration at one second period given in table 1-4 and 1-5 of chapter 1 of FME 356-2000. And the end pushover data command should be entered after all the pushover inputs so the loadings that are used to specify the pushover load so they need to be of the gravity load and push load type okay and so the load type is required and as i said so it should be either gravity or push so in all other means the program will give you an error okay so if there will be more than one gravity load case start pro will internally combine them all together in one case and use the combined gravity loading and you can have only one push load case and it can be in global X or Z direction and The combination of these directions is not allowed, so probably you'll have to use several input files. And also there are following limitations of pushover analysis input.
So you can have only one pushover analysis command and no change command accepted. There are no... print options for pushover analysis inside the perform analysis cluster and the load combinations not accepted.
Y-axis should be vertical. The concrete material is not considered and the cable members, plate, solid elements not considered, curved beams not considered and the beta angles should be either 0 or 90 degrees, everything else is not accepted and there are a few main modeling rules for the pushover analysis it is recommended to have some study of sensitivity of your model to the changes, so you can run the different properties and different structural elements and see how they react to changes in the, let's say, material properties or loading pattern and decide, find the best loading pattern for this specific model. And also the analysis results depend on the selection of control node.
And so the control node, the basic rule of thumb is that you specify the control node at the center of mass of the roof of the building. but it can also be at, let's say, any corner of the roof building. So, okay, so the basic scope of pushover analysis is that the buildings are regular and they don't have adverse distortion or multiple effects. So the capacity curve is constructed to represent the first mode of response of structure and the fully rigid frame and concentric braced frame are considered, so two types of frames. Only steel structure is considered and beams must be straight, beams and columns must be straight.
okay we consider only all members as primary elements and in case we will see that in the program but in case when you want to ignore the hinge development in some members you can specify hinge ignore command so we will see that later okay If user defines a hinge, so keep in mind that for columns only the deformation controlled action is considered as no actual force is considered for checking force controlled action in columns. By default, STAD will calculate the lateral pushload in positive X or Z global directions, and if someone wants to generate the pushloads in the negative global direction, so the command direction negative should be used. So, direction negative 1 will mean that the forces should be generated in the opposite direction. Okay, so let's jump into the application example. So I will share my screen and we will see how it looks like in Start Pro.
Okay, I have prepared two Start Pro inputs and one of them is initial input. So we have here a still frame with all the properties provided, specifications, so we see that there are member release specifications on the screen, we can see that, and let's go to the loading. There are already two load cases prepared in this input, so we will go for definitions and find the pushover definitions and press add. So we need to provide all the input information that we were speaking about before. So the type of frame, so the default one is Moment Frame and you can use the drop-down menu and select, let's say, Braced Frame, okay?
And you can include or ignore the geometric non-linearity effect, so I will use Include. Okay, so the optional parameters for convergence criteria for non- linearity I will leave that as default once I will not use them So here we see the saving options, so if you want to save the results, so you can, for multiple steps, you can specify the toggle the check marks here and specify for displacement incremental value, base share incremental value, and also you can print the output results, so if you put the check mark here so you can either step results either print result output for these three options can be printed in the output file okay i will not use that okay i will enter the member specific parameters so i will specify the yield stress so i don't want to use the default program yield stress but i will specify okay so I will specify 275 000 so 275 mega Pascal's that will be my yield stress and I will leave effective flame factors as default ones okay and I will add the parameter okay next we need to define the loading pattern I will use the user defined loading pattern since I have specifically created the push load case okay so I will leave everything as default but I will say that the number of push load steps I will set it to 25 okay and press odd next I need to define the spectrum details, so I will leave the first spectrum critical damping 5% as it is, so class D is okay, and I will set the short term period and one second period as 1 in both cases and press on okay. Next define the hinge properties. This time I will use the automatic FVMA specification.
and there are, if you will, enter the drop-down menu, so there is ignore option, as I mentioned, some members that will not develop the hinge, or may be ignored, you can ignore, so the hinge will not be formed in those members, also the hinge will not be formed in truss. members if you have trust specification so the hinges will not be formed in those members okay or you can use the user defined hinge properties and enter the data i will use fema and press add okay and the final step would be to define the solution control and i will ask to push up to define displacement and control joint so the displacement direction I will specify x-axis and let it be half a meter and the joint 706 and press Add so that's the current joint of the building far right corner joint so I specifically did not specify in the middle of the say at the center mass but just corner joint okay so we can now go and close we see some parameters are with a question mark so we need to assign them so I will go ahead and assign the yield stress to the view yes and the hinge will be assigned to you I'll go to select and I'll select group, group frame, okay and I will assign to selected beams assign and yes so these are my frame members where the hinges will be generated okay close let's review our load so this is the gravity load and if you double click on that I see that it's dead so that is not correct so we need to go and find the gravity so that should be specific loading type gravity modify close and the push load so it's correctly defined the loading type push load so i will go ahead and close so we can review the gravity load and we see that our push load is oriented in the x direction and that's the joint loads as start pro accepts that. So as we have done the changes, I will go to analysis and here we have already specified the pushover analysis.
So the pushover analysis is on the analysis print commands and it has no additional parameters. So if you press add and close, that appears in this list. So we can go and analyze.
So since the push-over analysis really takes some time so we can start it okay and you can see that it's calculating 4 6 7 10 11 percent and while it's running we can go into the analyzed model so this same input which we have entered here so it is already analyzed and after the analysis we go to the post-processing okay and the Pushover analysis results are available in the Dynamics tab, Layouts, Pushover, and we can go and review the loads. So how the loads were applied. So we can see, so this is the load step 1, and the load step 1 is no loads. Load step is, and we see here the base shear, and we cannot see that on the screen since since the arrows are too small, so it's few kilonewtons, if we go to scales and apply immediately and we will increase the arrows, so we see that, so load step 3, it's already 14 kilonewtons and we see that the base shear is as follows and we can see the load steps of the analysis completes in something like 2 minutes, about, maybe less, maybe more, so we will continue reviewing this model alright, so, and you can go ahead and see the loads, another results option here is graphs, so I will go and enable automatic scaling, apply, okay.
So here is our capacity curve, so you can see the, like in the manual, so you see the stride line which is our behavior, elastic behavior, then we see here small change in the curvature and that's the point B where the material starts yielding. So we see here, the target displacement, so 1974 inches, so that's probably our 0.5 meters, since the model was in imperial units, so we see here inches. Base shear at target displacement was 3275 kN. So we see here and then we see here a sudden drop so this means that plastic hinge reaches its capacity and the unloading appears and the loads are distributed on the other members so after the drop there is another nearly horizontal line so this means that the structure is distributing the loads to the adjacent other members and then again the plastic hinge capacity is superseded again drop so this means that it collapses and structure tries to distribute so this is our capacity curve so let's click with right mouse button on the graph and let's press determine target displacement ok and here we will find so number of stories so we have one two three four five six stories so it's something like between five and ten yes so that's and share buildings that's share buildings and the loading pattern was triangular load pattern so I will select value 1.3 from the table okay the other option is to define Okay, alright, I will click next.
So the damping 5% as we have selected and that's the number of stories free or more and that's still moment frame. Select that one. Okay, the CM value. Next.
Alright, so now we have to select the performance level of structure. Is it immediate occupancy, life safety or collapse prevention? So I will select immediate occupancy and that's the framing type 1 moment frame and press finish. Okay, so now the target displacement is 18.7 inches for this setup and the base share was 3000 kN.
Click with right mouse button again and press show idealized. capacity curve so the blue line is our idealistic capacity curve so so this is the point where our structure becomes unsafe okay so and you can see the displacement value at the idealized capacity curve 9 inches and the base shear is 6000 kN something like that, so 6381 ok, so the next one so can we change the values let's say to you all right I cannot change the values so probably need to change inches to meters or something somewhere else okay next one is node results so here we can here we can see the node the displacements at each step, so let's say, so we can move the reservoirs and we see with each step what are the displacements and rotations and the support reactions, so step 27, base shear is 5835 kN, okay, so maximum load steps 96 and nodes, support nodes, and we see the support reactions at each step. Okay? And the fourth option for pushover analysis results is beam hinge results. And here it is very useful from the point of view so you can find out at which step and which loading the hinges are formed.
So step 5, so you can see that the green dot representing the hinge, so the first hinges are formed at this member beam number 31, so you can see that and it's still linear behavior, so the status is linear but there is a hinge, it's linear Alright, so next, green bubbles appearing with the tapes, and if we go further, so you can see that the nonlinear PIM37 and its nonlinear behavior already in Z direction, and it is less or equal than immediate occupancy status. and if we go further, some more hinges appear and let's find some of the blue dots so we have found some blue dots, so this one, it's non-linear hinge and the status is between immediate occupancy and life safety already and if we move further, so we can try and find when... yeah, so the magenta color here, for example, first column here, this one and that's the nonlinear status and between life safety and collapse prevention so the first column to fail is probably this one so it's reaching that limit okay and okay so step number 59 so it loads step 59 this column shows in red so this means that it's inactive already okay so it's collapsed so you can see that in this table right So it's already collapsed and the loads are distributed to adjacent members, so the load carrying capacity is zero of this member. It's no longer here, and if we will continue, so we will see the hinges appearing in our members. Okay, so the second column.
So reaching step number six, so the second column is losing its carrying capacity, so it becomes inactive too. Okay, so this was a live example of showover analysis in Start Pro.