1         INTRODUCTION

1.1        OVERVIEW

The purpose of this document is to provide an introduction to the procedures that are required for performing a non-linear blast analysis using SACS. The procedures are presented in tandem with a sample analysis based on a hypothetical model that contains structural elements that would be typical of a quarters building. The blast loading is developed using an over-pressure profile that is based on guidelines presented in the publication ‘Design of Blast Resistant Buildings in Petrochemical Facilities’, prepared by the Task Committee on Blast Resistant Design of the American Society of Civil Engineers.

1.2        ANALYSIS OBJECTIVE

The objective of the analysis is to determine the survivability of a quarters building and the support framing following an explosion. The quarters building and support framing for a hypothetical structure are evaluated for blast loading resulting from an explosion occurring near the building. The building and support frame are blast-loaded using techniques for overpressures outlined in the publication ‘Design of Blast Resistant Buildings in Petrochemical Facilities’. The following figure shows the structure used for the blast, along with the blast location.

1.3        BLAST PROFILE PARAMETERIZATION

The blast pressures and profiles are developed based on an idealized equivalent pressure load outlined in ‘Design of Blast Resistant Buildings in Petrochemical Facilities’. The following profile illustrates how a typical blast wave is parameterized:

Where:

P_r – Reflected overpressure

C_r – Reflection coefficient

P_so – Side-on pressure

P_s – Stagnation Pressure

The stagnation and reflected over-pressures are calculated using the following formulae:

Where:

P_s – stagnation pressure

q_o – peak dynamic wind pressure

C_d – drag coefficient

t_c – clearing time taken as 3(S/U) where S is the minimum of H or B/2

t_d – over-pressure duration

U – shock front velocity

2         ANALYSIS DESCRIPTION

2.1        MODEL DESCRIPTION

The SACS model includes the quarters building and support framing. The model also includes the building wall, roof and floor plating for stiffness purposes. The quarters building comprises plates that are approximately 1 cm thick and are stiffened with box sections that run vertically. The quarters building dimensions are approximately 6.5m wide, 3.4m high and 12.6m in length. The panels have a yield stress of 24.8kN/cm². The framing contains tubular members of various dimensions. In particular, the support columns have OD of 45 cm and a thickness of 2cm. The columns have a yield stress of approximately 35kN/cm². The plates that constitute the building quarters are kept elastic. For the purpose clarity, the base of each of the support columns is fully constrained.

2.2        LOADING ASSUMPTIONS

The model is subjected to two sets of loads. Firstly, a static load of approximately 610kN is applied in order to represent the self-weight of the structure. Subsequently a pressure load is then applied incrementally in order to represent the blast wave that is incident on the front wall. At its peak, the reflected over-pressure is 120kPa which results in a total front-wall load of 2850kN. Typically, additional loads could be considered for the static loading, (such as live loads). Furthermore, the blast wave would ordinarily impact the side walls, roof and rear wall as well as the support frame. However, for reasons of clarity, only the front wall is loaded and the sole static load is the self-weight.

2.3        BLAST PROFILE

The following blast profile has been adopted for the front wall. The profile defines a (peak) reflected over pressure of 120kPa after 0.015 seconds and a clearing pressure of 48kPa at the reflected over-pressure clearing time at 0.029 seconds. The total duration of the over-pressure is 0.2 seconds after which only residual loading from the inertia forces occurs. The entire blast event is modeled for a total of 5.0 seconds. The time step increment is 0.025 seconds.

3         ANALYSIS PROCEDURE

3.1        OVERVIEW

The analysis procedure entails six steps:

• Define a self-weight load condition (DEAD)
• Define a pressure load condition that corresponds to the peak blast wave overpressure (BL01)
• Create a blast profile in a dynamic response input file
• Define a Collapse input file that references the self-weight load condition and other static load conditions
• Create mode shape and mass matrix information using DYNPAC
• Perform a forced response analysis (which in turn runs Dynamic Response and Collapse)

The procedure is now described in detail.

3.2        SELF-WEIGHT

The self-weight load condition, DEAD, is generated in Precede using the Load > Self Weight menu item.

3.3        PRESSURE LOAD

The pressure load condition corresponding to the peak blast wave over-pressure is generated in Precede. The Load > Pressure > Plate Area menu item was used with a constant pressure of 120kPa being applied in the global Y-direction to the plates of the front wall.

3.4        BLAST PROFILE (DYNAMIC RESPONSE INPUT FILE)

The blast load time history is defined in the Dynamic Response input file using LOADC lines. The ‘CLP’ on the DROPT line indicates that inertia loads are to be generated for a force-time history Collapse analysis. Two percent structural damping was used in conjunction with linear time history interpolation. The analysis time considered was 5 seconds with load increments every 0.025 seconds.

The LOADC lines refer to the pressure load condition. They describe a ramp force-time history by applying a load factor a certain points in time. For example, the peak reflected over-pressure occurs at time 0.015 seconds, which corresponds to 100% of the BL01 load condition. The clearing pressure is only 40% of the peak over-pressure, which corresponds to a load factor of 0.4 at the clearing time of 0.029 seconds.

3.5        COLLAPSE INPUT FILE

Prior to running the analysis, a partial Collapse input file is specified in order to control the non-linear solution phase. The Collapse input file is used to:

• provide control data for the Collapse run.
• start the definition of a Collapse load sequence called BLST.

The collapse options are specified on the CLPOPT line as follows:

The effect of strain-hardening is considered for any element in which plasticity has occurred. The strain hardening ratio, taken as the ratio of the slope of the plastic portion or the stress strain curve to the slope of the elastic portion, is designated as 0.05. A maximum of 50 iterations is allowed per increment, the deflection tolerance is 0.1cm and the rotation tolerance is 0.01 radians. In the event that convergence has not been achieved for a particular increment, the ‘CN’ option ensures that the analysis will continue. In the event that continuation arises after non-convergence, it is advisable to closely inspect the results at the relevant increment. The start of the blast load sequence is now defined. The static loads should be defined prior to the dynamic blast load event. The load sequence is started with an LDAP line. In the following, the LDAP line specifies that 100% of the self-weight load condition (DEAD) should be applied. The ‘1’ indicates that the load should be applied using 1 load increment.

The remainder of the load sequence is automatically generated for the user from information given for the blast profile in the Dynamic Response input file. Nominal yield strength is used for the purposes of this study. Although yield stress strength and dynamic increase factors that incorporate the effect of material strength increase with strain rate is appropriate, effective yield stress increase is conservatively not considered for this analysis. However, Collapse has a number of yield stress over-ride capabilities that allow for the implementation of dynamic increase factors as follows:

YSFACT                Universal yield stress factor

YSUOVR               Universal yield stress over-ride

YSUMOD             Modification of Yield stress by value

YSMGOV             Override the yield stress by member group

3.6        MODE SHAPE AND MASS MATRIX CREATION

The mode shapes and mass matrix are required in order to run the analysis. This is easily achieved by using ‘Extract Mode Shapes’ from the Dynamic Analysis section of the Executive Runfile Wizard. Use the ‘Modal Extraction Options’ method, which will avoid the need for an input file. Select the ‘Consistent Distributed’ mass lumping method and specify that 20 mode shapes are extracted.

3.7        FORCED RESPONSE ANALYSIS

The non-linear blast analysis can now be run. This can be accomplished by selecting ‘Forced Response’ from the Dynamic Analysis section of the Executive Runfile Wizard. The user is prompted for a sequence of input files as follows:

• A dynamic response input file. Use the file that was discussed in Section 3.4. The Executive recognizes that the intended analysis is for a force-time history Collapse analysis and will prompt the user to see if Collapse should be launched automatically. In this case, check the box in order to say ‘yes’.
• A SACS input file.
• A Collapse input file. Use the Collapse input file discussed in Section 3.5. Once the analysis is underway, Dynamic Response will create a new Collapse input file.
• The mode shape and mass matrix file.

After all the input files have been specified, the forced response analysis will be launched, which entails a dynamic response run, followed by a Collapse run. There are a number of events that take place automatically. These events are now discussed.

The Dynamic Response run will take the original SACS input file and append a number of load conditions. Each load condition contains applied force and inertia force information that will eventually be used by Collapse to perform an incremental non-linear blast analysis. The extra load conditions are created in the Dynamic Response output structural data file (DYROCI).

Furthermore, Dynamic Response will create a new Collapse input file (CLPINA) containing a load sequence that references the new load conditions in the output structural data file.

A flow chart that describes the information flow, along with the constituent SACS programs is presented below:

4         BLAST ANALYSIS RESULTS

4.1        RESULTS INSPECTION

The results of the analysis may be inspected by launching 3D Collapse Viewer. In the first instance, the loading on the structure is verified by plotting the total Y-direction force that is applied to joint ‘215’ against the load step. The applied force due to the blast wave can be seen during the first fraction of a second. After load step 8 (which corresponds to 0.2 seconds), the blast wave over-pressure phase is over. Any loading thereafter is due to the oscillatory inertia forces.

4.2        SPECIAL EVENT HISTORY REPORT

3D Collapse Viewer provides a simple method for determining noteworthy events that have occurred during a load sequence. The special event history report is accessible under the Report Selection () > History menu item. A section from the special event history report of this analysis is shown below.

The report highlights a number of plasticity events. It demonstrates that the onset of plasticity occurs at load step 4 (0.1 seconds). The final plastic event occurs at load step 12 (0.3 seconds). The significance of these events is that the plasticity of the members begins sometime after the peak of the blast loading (0.015 seconds). The final plastic event occurs .1 seconds after the end of the positive over-pressure. For this particular analysis, it suggests that the inertia forces have played a considerable role in the response of the structure to the blast loading.

4.3        PLATE STRESS REPORT

Collapse View provides a simple report on plate stresses throughout the load sequence. The report may be accessed through the Report > Plate > Stresses menu item. For this analysis, the report indicates that the peak combined plate stress is 1.77kN/cm² , and that this occurs in plate QF09 at load step 2.

4.4        RESULTS VISUALIZATION

A snap-shot of the entire structure at load step 12 provides a visible confirmation that the support columns have undergone plastic loading, as evidenced by the coloration.

4.5        VISUALIZATION OF PERMANENT DEFORMATION

Finally, a graph is plotted of the Y-displacement for joint ‘215’ against the load step. It can be seen that as the load sequence progresses, the displacement of the joint is converging in an oscillatory manner to a final value of approximately 3 cm. This is yet another indication of the non-linear plastic behavior of the structure that has occurred after the initial blast and demonstrates that a small amount of permanent deformation has occurred. Subsequent to load step 12, there is visible symmetry in the displacement peaks when centered about the permanent deflection value. This provides more evidence that the major plasticity events have occurred prior to load step 12, and that structural loading and unloading thereafter is elastic in nature.

 

4.6        REFERENCES

[1]          ‘Design of Blast Resistant Buildings in Petrochemical Facilities’, prepared by the Task Committee on Blast Resistant Design of the American Society of Civil Engineers.

[2]          SACS Collapse Manual.

[3]          SACS Dynamic Response Manual.

[4]          Analysis Input Files: sacinp.blast, clpinp.blast, dyrinp.blas

 communities.bentley.com/.../Blast-Analysis-Input-Files.zip