13.6 Impact Loading

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Impact effects on structures arise over a very broad range of circumstances, from high-velocity missiles or

aircraft impact to high-mass ship or vehicle collisions. The requirement may be for the structure to

withstand the impact without serious damage, or major inelastic deformation may be permitted.

13.6.1 Structural Impact between Two Bodies — Hard Impact

and Soft Impact

Impact loads differ from blast loads in duration, and they are applied to a localized area. Blast loads

propagate as a wave front, while an impact load is caused by the force resulting from the collision between

a moving object and a structure. Impact loading can be classified as either hard or soft, depending upon

the relative characteristics of the impactor and the target structure. Impulsive loading can be considered

to be a special case of soft impact. Soft impact occurs when the impactor deforms substantially with

respect to a hard structure, and a portion of the impactor’s kinetic energy is absorbed by the impactor’s

plastic deformation. For hard impact, the striking object is rigid and the kinetic energy is transmitted to

the target and absorbed by deformation and damage in the structure.

Impact problems essentially involve all three fundamental conservation laws: conservation of mass,

conservation of momentum, and conservation of energy. These three laws are outlined in the following

equations (Zukas, 1990), respectively

ð

v

r dV ¼ const ð13:43Þ

X F ¼ m dv=dt ð13:44Þ

Ei þ

X 1

2

rv2

i ¼

X

Ef þ

X 1

2

rv2

f þ W ð13:45Þ

where

r ¼ material density

V ¼ volume

F ¼ force

TABLE 13.8 Examples of Computer Programs Used to Simulate Blast Effects and Structural Response

Name Purpose and Type of Analysis Author/Vendor

BLASTX Blast prediction, CFDa SAIC

CTH Blast prediction, CFD Sandia National Laboratories

FEFLO Blast prediction, CFD SAIC

FOIL Blast prediction, CFD Applied Research Associates, Waterways Experiment Station

SHARC Blast prediction, CFD Applied Research Associates, Inc.

DYNA3D Structural response, CFD (coupled analysis) Lawrence Livermore National Laboratory (LLNL)

ALE3D Coupled analysis Lawrence Livermore National Laboratory (LLNL)

LS-DYNA Structural response, CFD (coupled analysis) Livermore Software Technology Corporation (LSTC)

Air3D Blast prediction, CFD Royal Military Science College, Cranfield University

CONWEP Blast prediction (empirical) U.S. Army Waterways Experiment Station

AUTODYN Structural response, CFD (coupled analysis) Century Dynamics

ABAQUS Structural response, CFD (coupled analysis) ABAQUS Inc.

a CFD, computational fluid mechanics.

Vibration and Shock Problems of Civil Engineering Structures 13-47

© 2005 by Taylor & Francis Group, LLC

m ¼ mass

v ¼ velocity

E ¼ stored internal energy

W ¼ work

i, f ¼ initial and final states

Upon impact, stresses and strains are induced in the target material. The layers of particles in the target

are compressed upon contact, creating compressive stress. When the compression stress between two

layers is equal to the applied pressure, compression supports the entire pressure. Through this process,

stress waves are developed similar to the shock waves generated by blast loading. The stress waves

propagate throughout the material at a speed inherent to that material and reflect multiple times as

interfaces are reached.

Various types of stress waves are developed, depending on the energy imparted into the target.

The impact velocity determines the strain rate, mode of response, and the type of impact damage

(Zukas et al., 1982). If the impact is below a certain level, only elastic stress waves are generated. Higher

velocity impacts create inelastic stress waves. Historically, impact has been considered a localized

phenomenon that may cause plastic deformation and/or failure of the target and/or the impactor. During

an impact event, some or all of the kinetic energy of the impactor is transferred to the target. This process

is a function of the wave propagation in the target, the impactor’s deformation of the target upon contact,

and the contact velocity. Because the impact has been considered to be localized, the local behavior

deformation and penetration has been the prime consideration.

Impact causes elastic and plastic stress waves, and propagation through the structural thickness can

cause failure by spalling. Such effects usually occur within microseconds of the impact, and may be

referred to as the early time response. The overall dynamic response of the structure usually occurs on a

timescale several orders of magnitude longer, and can thus reasonably be decoupled from the early time

response and subjected to an initial check against spalling.

Impact imparts impulsive loadings to a structure, producing responses within the structure. Three

different types of solutions to the impact problem are available: theoretical (analytical), semiempirical,

and numerical. Theoretical methods provide closed-form solutions for the governing partial differential

FIGURE 13.31 Transient deformation of a reinforced concrete beam under impact at midspan. (Source: Data from

Ngo, T. et al., Proc. of 18th Australasian Conference on the Mechanics of Structures and Materials, Perth, Australia. 2004a.

With permission.)

13-48 Vibration and Shock Handbook

© 2005 by Taylor & Francis Group, LLC

equations. Semiempirical methods rely on extensive test data to produce a curve-fit solution for a class of

similar impact problems. Numerical solutions replace the continuous system with discrete domains and

treat the problem as it progresses over time (Figure 13.31).

13.6.2 Example — Aircraft Impact

Design loads resulting from aircraft impacts are governed by the absorption of kinetic energy from the

aircraft by the building at its maximum deflection. These loads are limited by the yield, buckling,

and crushing of the aircraft. Total impact load FðtÞ at the interface of the collapsing aircraft and the

building is given by

FðtÞ ¼ Fc þ m½mðtÞ􀀉V ðtÞ ð13:46Þ

in which mðtÞ is the mass of the aircraft reaching the building per unit time; m is a coefficient for change

in momentum (which can be taken conservatively as one); Fc is the crushing load, a constant which can

be determined from the design acceleration for failure of the aircraft; and V ðtÞ is the velocity of the

aircraft.

Figure 13.32 compares the impact loads produced by a Boeing 707-320 and a Boeing 767, which hit the

World Trade Center. It should be noted that World Trade Center was designed to resist the equivalent

impact of a Boeing 707.

Figure 13.33 compares the impact loads produced by different aircraft. The peak loads and the

duration of loading for different aircraft are given in Table 13.9. These loads were calculated by the

method suggested by Kar in 1979 (Mendis and Ngo, 2002).

Kinsella and Jowett (1981) suggested a more accurate method in which the crash event is treated

as a combination of the separate time-dependent impacts of the aircraft’s frame and engines. The

frame is classed as a soft missile which will suffer considerable deformation, and a finite difference

method of calculation is employed to describe its perfectly plastic impact. The engines, which are

considered separately, are assumed to constitute a much harder missile which will undergo little

deformation. The results obtained by this method for a Phantom F4 aircraft are shown in Figure

13.34. This method gave a maximum load of 233 MN compared with the 145 MN obtained from

Kar’s method.

Impact Load, P (kN × 103)

t (sec)

0.1 0.2 0.3 0.4

100

200

300

Boeing 767, V = 140 m/s

Boeing 707,V = 100 m/s

FIGURE 13.32 Impact load – time history for aircraft impact.

Vibration and Shock Problems of Civil Engineering Structures 13-49

© 2005 by Taylor & Francis Group, LLC

TABLE 13.9 Examples of Aircraft and Peak Impact Loads

Aircraft Mass

(kg)

Length

(m)

Velocity V0

(m/sec)

Peak Load

(MN)

Duration

(msec)

Aust. SUPAPUP light aircraft 340 5.7 51.3 4.6 111

Westland Sea King helicopter 9,500 17 63.9 19.6 266

Boeing 707-320 91,000 40 103.6 92 386

Phantom F4 aircraft 22,000 19.2 210 145 91

Boeing 767-300 ER 187,000 54.9 140 320 362

Supersonic Concorde 138,000 62.2 344 568 181

Load-time history

0

100

200

300

400

500

600

700

0 50 100 150 200 250

time (msec)

Impact load, P (MN)

Concorde

Boeing 767

B707

F4

Light aircraft Helicopter

FIGURE 13.33 Comparison of impact loads for different aircraft.

Predicted Load-time history

233

49.1

0

50

100

150

200

250

0 20 40 60 80 100

time in ms

F (t) in MN

Air Frame

Engine

Total

impact

FIGURE 13.34 Impact loads of Phantom F4 aircraft. (Source: Data from Kinsella, K. and Jowett, J. 1981.

The Dynamic Load Arising from a Crashing Military Combat Aircraft, Safety and Reliability Directorate, Wigshaw, U.K.

With permission.)

13-50 Vibration and Shock Handbook

© 2005 by Taylor & Francis Group, LLC

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