Pressure–Time Histories, Peak Pressure & Impulse

Why the Whole Time History Matters

A pressure-time history contains more structural information than any single scalar. Peak pressure influences local acceleration and early yielding; duration controls how long the structure is driven; impulse controls net momentum transfer; rise time and decay shape influence high-frequency content and local response. Reducing a supplied history to “peak pressure only” or “impulse only” may be appropriate for a particular response regime, but that is a modelling decision that must be justified against the relevant structural period and failure mode.

Peak Pressure Is Not a Universal Severity Measure

A short, high peak can produce less global displacement than a lower pressure acting for longer, while still creating more severe local stress or support reaction. The opposite can occur for a flexible system whose response is governed mainly by accumulated impulse. This is why comparing two blast cases by peak alone can rank them incorrectly. The analyst should compare the complete histories or at minimum peak, duration, impulse, spatial distribution and their relation to the structure’s dynamic characteristics.

Impulse Represents Integrated Pressure, Not Structural Work

Impulse is the time integral of pressure and is closely related to momentum transfer, but it is not the energy absorbed by the structure. Structural work depends on force acting through displacement, including the phase relationship between load and motion. Two pulses with equal impulse can perform different work if their timing relative to the structural response differs. This distinction matters when comparing pulses, selecting equivalent triangular histories or judging whether an impulse-based simplification is adequate.

Pressure impulse:  I_p = ∫ p(t) dt

Applied-force impulse on a uniform loaded area A:  I_F = A ∫ p(t) dt

Energy absorbed by the structure is not I_F; it depends on ∫ F(t) · v(t) dt.

Pulse Duration Relative to Natural Period

The non-dimensional ratio of significant load duration to structural period is more informative than duration alone. If the pulse is very short relative to the mode controlling the response, the structure receives momentum before substantial displacement occurs. If the pulse is long, displacement develops while pressure remains applied. Intermediate cases are often most sensitive to detailed pulse shape. Because a structure has many modes, one load case can be impulsive for the global frame but pressure-controlled for a small local panel.

Rise Time and Early-Time Content

An idealised instantaneous pressure rise contains very high-frequency content. Real supplied histories may have finite rise time because of the environment, measurement bandwidth or hazards-model resolution. Replacing a finite rise with an instantaneous step can increase high-frequency local response, while excessive smoothing can remove genuine early-time demand. The appropriate treatment depends on whether local wave effects, panel modes or only lower-frequency global response are important. Any filtering should therefore be justified against both the load data and structural bandwidth.

Equivalent Pulse Idealisation

Simple triangular, bilinear or piecewise-linear histories can be useful for SDOF calculations and model verification. The equivalent pulse should preserve the quantities relevant to the chosen response regime—often peak and impulse, but sometimes duration or initial rise as well. Matching area under the curve alone is not enough if local yielding is governed by the peak. Conversely, matching peak alone can badly misrepresent global displacement. The simplified and original histories should be compared in at least one representative structural model before the idealisation becomes a production assumption.

Resampling and Numerical Application

Pressure data may arrive with a time increment much finer or coarser than the structural solver requires. Resampling should preserve extrema, impulse and meaningful frequency content. Interpolation can shift a sharp peak; decimation can reduce impulse; extrapolation beyond the supplied range can create artificial loading. For explicit analysis, the structural stable time increment can be much smaller than the pressure-data interval, in which case the solver interpolates the applied load. Verify the interpolated curve actually seen by the model rather than assuming the input table is reproduced exactly.

Positive and Negative Pressure Portions

Some specified blast histories include a subsequent negative-pressure portion. Its significance depends on structural period, residual motion, support conditions and whether the structure has already yielded or separated. The negative phase can reduce one response measure while increasing reverse displacement or connection demand. It should not be deleted automatically, nor should it be included mechanically when the governing hazard definition explicitly excludes it. Treat it as part of the controlled load specification and test its significance where uncertain.

Verification of an Applied Pressure History

Verification should compare the source history and the pressure actually applied to representative model faces. Integrate both to check impulse, confirm the sign convention, inspect onset and termination times and sum surface forces to verify the intended resultant. For spatially varying fields, repeat the check at multiple zones and compare total force and moment histories. These simple checks catch unit conversion, interpolation, area weighting and orientation errors that a sophisticated nonlinear solution will not detect.

• Peak pressure reproduced
• Integrated impulse reproduced
• Rise, duration and sign preserved
• Applied resultant force/moment checked
• Structural response checked against an independent idealisation

Engineering Outcome

A pressure-time history should be simplified only after establishing which aspects of it control the structural decision. The aim is not to retain every digit in the hazards dataset; it is to preserve the parts of the load that determine acceleration, deformation, yielding, connection demand and residual integrity for the structure being assessed.

Key takeaways

• Peak, duration, impulse and pulse shape influence different aspects of response.
• Use equivalent pulses only when their structural equivalence has been demonstrated.
• Verify the pressure history actually applied by the solver, not just the source table.