6.3.4 Direct Design Methods

The direct design approach (Figure 6-5) to be used for the structural protective measures is to first design the building for conventional loads, then evaluate the structure’s response to explosive loads and augment the design, if needed. Finally, the designer must make sure that all conventional load requirements are still met. This approach ensures that the design meets all the requirements for gravity and natural hazards in addition to air-blast effects. Take note that measures taken to mitigate explosive loads may reduce the structure’s performance under other types of loads, and therefore an iterative approach may be needed. As an example, increased mass generally increases the design forces for seismic loads, whereas increased mass generally improves performance under explosive loads. Careful consideration between the protective design consultant and the structural engineer is needed to provide an optimized design.

Nonlinear dynamic analysis techniques are similar to those currently used in advanced seismic analysis. Analytical models range from handbook methods to equivalent single-degree-of-freedom (SDOF) models to finite element (FE) representation. For SDOF and FE methods. numerical computation requires adequate resolution in space and time to account for the high-intensity, short-duration loading and nonlinear response (Figure 6-6). Difficulties involve the selection of the model and appropriate failure modes, and finally, the interpretation of the results for structural design details. Whenever possible, results are checked against data from tests and experiments for similar structures and loadings.

Charts are available that provide damage estimates for various types of construction, as a function of peak pressure and peak impulse, based on analysis or empirical data. Military design handbooks typically provide this type of design information.

Components such as beams, slabs, or walls can often be modeled by a SDOF system and the governing equation of motion solved by using numerical methods. There are also charts available in text books and military handbooks for linearly decaying loads, which provide the peak response and circumvent the need to solve differential equations. These charts require only knowledge of the fundamental period of the element, its ultimate resistance force, the peak pressure applied to the element, and the equivalent linear decay time to evaluate the peak displacement response of the system. The design of the anchorage and supporting structural system can be evaluated by using the ultimate flexural capacity obtained from the dynamic analysis.

For SDOF systems, material behavior can be modeled using idealized elastic, perfectly-plastic stress-deformation functions, based on actual structural support conditions and strain-rate-enhanced material properties. The model properties selected provide the same peak displace ment and fundamental period as the actual structural system in flexure. Furthermore, the mass and the resistance functions are multiplied by mass and load factors, which estimate the actual portion of the mass or load participating in the deflection of the member along its span.

For more complex elements, the engineer must resort to finite-element numerical time integration techniques and/or explosive testing. The time and cost of the analysis cannot be ignored when choosing design procedures. Because the design process is a sequence of iterations, the cost of analysis must be justified in terms of benefits to the project and increased confidence in the reliability of the results. In some cases, an SDOF approach will be used for the preliminary design, and a more sophisticated approach using finite elements, and/or explosive testing may be used for the final verification of the design.

A dynamic nonlinear approach is more likely than a static approach to provide a section that meets the design constraints of the project. Elastic static calculations are likely to give overly conservative design solutions if the peak pressure is considered without the effect of load duration. By using dynamic calculations instead of static, we are able to account for the very short duration of the loading. Because the peak pressure levels are so high, it is important to account for the short duration to properly model the structural response. In addition, the inertial effect included in dynamic computations greatly improves response. This is because by the time the mass is mobilized, the loading is greatly diminished, enhancing response. Furthermore, by accepting that damage occurs it is possible to account for the energy absorbed by ductile systems through plastic deformation. Finally, because the loading is so rapid, it is possible to enhance the material strength to account for strain-rate effects.

In dynamic nonlinear analysis, response is evaluated by comparing the ductility (i.e., the peak displacement divided by the elastic limit  displacement) and/or support rotation (the angle between the support and the point of peak deflection) to empirically established maximum values that have been established by the military through explosive testing. Note that these values are typically based on limited testing and are not well defined within the industry at this time. Maximum permissible values vary, depending on the material and the acceptable damage level.

Levels of damage computed by means of analysis may be described by the terms minor, moderate, or major, depending on the peak ductility, support rotation and collateral effects. A brief description of each damage level is given below.

• Minor: Nonstructural failure of building elements such as windows, doors, cladding, and false ceilings. Injuries may be expected, and fatalities are possible but unlikely.
• Moderate: Structural damage is confined to a localized area and is usually repairable. Structural failure is limited to secondary structural members such as beams, slabs, and non-load-bearing walls. However, if the building has been designed for loss of primary members, localized loss of columns may be accommodated. Injuries and possible fatalities are expected.
• Major: Loss of primary structural components such as columns or transfer girders precipitates loss of additional adjacent members that are adjacent to or above the lost member. In this case, extensive fatalities are expected. Building is usually not repairable.

Generally, moderate damage at the design threat level is a reasonable design goal for new construction.