process. since impact loading on concrete …...design concept for reinforced concrete slab...

Design concept for reinforced concrete slab

structures under soft impact loads

A Miyamoto', M.W King*

° Department of Computer and Systems Engineering,

Yamaguchi University, Tokwa-dai 2557, Ube 755, Japan

Boral Concrete Sdn. Bhd., Taman Sri Tunas,

Bay an Lepas, 11950 Penang, Malaysia

Abstract

The main objective of this paper is to propose a dynamic design procedure forconcrete slab structures to soft impact loads. Firstly, the ultimate limit states ofconcrete structures are briefly introduced. And then, a design procedure forreinforced concrete(RC) slab structures under impact loads is discussed based onenergy criterion and load criterion. Finally, a few case studies on design of RCslab structures are carried out as an example of the proposed dynamic designprocedure.

1. Introduction

Impact design methods of most structures are carried out by adopting an impactfactor in the static design method. The dynamic forces during impact areconverted into a static force of equal magnitude and treated in much the sameway as other static loads. This static design method would not adequatelydescribe an impact phenomenon and thus have only a limited amount of practicalapplicability. During impacts, an excitation of not only the first mode but alsohigher modes of vibration can be expected. Structures designed using theequivalent dynamic force would be able to withstand bending but not the shear,hence bringing about punching shear or concrete scabbing. These factors canonly be totally considered if a dynamic design approach is adopted.

In this paper, a design procedure for concrete slab structures under impactloads is discussed based on both energy criterion and load criterion. In theproposed dynamic design procedure, the indexes for impact resistance, such asimpact load at failure, total energy, index of local deformation, volumedisplaced, etc.fl] are employed for determining structural modificationsnecessary in the design procedure. Furthermore, a case study of design ofreinforced concrete guardrail(handrail) under vehicular collision is carried out asan example of the proposed dynamic design procedure.

2. Ultimate States of Concrete Structures

The ultimate states of a concrete structure are necessary during the design

Transactions on the Built Environment vol 22, © 1996 WIT Press, www.witpress.com, ISSN 1743-3509

792 Structures Under Shock And Impact

process. Since impact loading on concrete structures has a very low occurrenceprobability, the normal case would be to design the structure according to theultimate limit states. A serviceability limit state would results in anuneconomical and conservative design. The ultimate states for different types ofconcrete structures are totally different. Some examples of ideal ultimate limitstates for concrete structures in the field of civil and structural engineering arelisted in Table 1. The ultimate limit state for rock sheds under impact loadingcan be set as structural failure, either in the bending or shear failure modes. Butin the case of concrete handrails, the ultimate limit state would also be structuralfailure. But the resultant impact failure mode would be a very important factor.Another limit state for concrete handrails, especially in overhead expressways or

Table 1: Ultimate states of concrete structures under impact loads

Loadcharacteristic

Soft

Hard

Impactor

Vehicle

Ship

Aircraft

Rock

Explosion

Target / Structure

Handrail / Barrier

Building

Bridge pier

Bridge girder

Bridge pier

Offshore structureMarine structureGravity platform

Nuclear power plantImportant structureProtective shelter

Rock /Snow shed

Protective shelter

Ideal ultimate limit states

Failure in structural element. Energy is absorbed byflexural deformation of structure. Punching shear andconcrete scabbing should be prevented.

Energy is absorbed by failure in structural element.Collapse of entire structural system should be preventedby allowing hinges to form at beam sections.

Energy is absorbed by failure in structural element. Butthe stability of entire structure should be ensured,especially in the supporting forces. Furthermore,deformations that would cause movements to the upperstructure should be checked.

Failure in structural element. Large deformations wouldcause collapse of the girders from piers. Adequateflexibility should be allowed to prevent collapse fromsupporting piers.

Energy is absorbed by failure in structural element. Butthe stability of entire structure should be ensured,especially in the supporting forces. Furthermore,deformations that would cause movements to the upperstructure should be checked. At deep water levels, thepiers should be designed to be rigid, i.e., collisionenergy should be absorbed by deformation of ship.

Energy is absorbed by failure in structural element. Butthe stability of entire structural stability should beensured.

Single layered structure: Cracks should not be allowedfor structures of extreme importance. In certain cases,cracking should be allowed but penetration andscabbing should be prevented at all cause.Double protection structure: Penetration and scabbingare allowable in the secondary structure. Cracks shouldnot be aJ lowed in the primary structure for extremelyimportant structures. In certain cases, cracking shouldbe allowed but penetration and scabbing should beprevented ai all cause in the primary structure.

Failure in structural element.

Single structure: Cracks should not be allowed forstructures of extreme importance. In certain cases,cracking should be allowed but penetration andscabbing should be prevented at all cause.Double protection structure: Penetration and scabbingare allowable in the secondary structure. Cracks shouldnot be allowed m the primary structure for extremelyimportant structures. In certain cases, cracking shouldbe allowed but penetration and scabbing should beprevented at all cause in the primary structure.


Structures Under Shock And Impact 193

in multi-story intersections (crossings), is the prevention of scabbing at the rearface, as concrete scabbing would likely cause a secondary disaster when fallingonto a different traffic lane below. Concrete scabbing can be effectively reducedor even prevented by allowing a bending failure mode to occur. The formation ofshear cones during shear failure would cause concrete scabbing to occur easily.Therefore, for the design of concrete handrails, the bending failure mode wouldbe important.

A different ultimate state would be for the design of nuclear power plantsand its related facilities, where cracking in the concrete structure could causeleakage of radioactive materials into the atmosphere. In certain cases, where thestructure is not highly radioactive, then prevention of perforation would be amore economical ultimate state. Structural integrity would be a major ultimatestate when considering a structural system. For example, in the design of marineoffshore structures or gravity platforms, or even the design of buildings, failureof structural elements would be the limit state, but the total structure should beintact after the impact. A loss in the bearing capacity of a structural elementcould cause the entire structure to collapse.

The amount of permanent deformation is also the ultimate limit states incertain cases. For example, the permanent deformation in a bridge pier should belimited, or else it would cause damage or even collapse of the super-structure.

The ultimate states for reinforced concrete handrail will be discussed alittle more in detail here and followed by a case study for design in the followingsection. An ideal design procedure of concrete handrails for expressways isrelatively difficult. An ideal handrail should be able to withstand the impactfrom a colliding vehicle. The handrail should not act as a solid barrier to stop thecollision but more as a flexible wall that is capable of absorbing most of theimpact collision energy. Therefore, it is necessary to design concrete handrails tofail under bending, as energy absorption is better during ductile type of failure.During the collision of a light vehicle or when the impact momentum isrelatively small, the handrail should act as a rigid barrier and allow thedeformation of the vehicle itself to absorb most of the impact energy. When themomentum of the collision is large, or when the collision speed is large, then thehandrail should deform and absorb most of the impact energy, especially in thebending mode, and possibly let the vehicle not to have relatively largedeformations. Therefore, the life or lives of occupants in the vehicle would notbe highly endangered. In the case of collisions by large trucks or trailers, thestructure should absorb the energy but not allow scabbing of concrete to occur atthe rear face.

3. Design Concepts for Reinforced Concrete Structures

The energy criterion would be the most efficient method of designing concretestructures under impact loads. The external energy from the impacting body(impactor) should be absorbed by the entire structure. The energy transformationprocess during impact loading of concrete structures is illustrated in Figure l[2j.The main part of the kinetic energy in an impacting body is transmitted to theconcrete structure during impact collision. The energy transmitted to theconcrete structure is then converted into the kinetic energy of the concretestructure and also the energy absorbed by the structure. The energy absorbed bythe structure is converted into irrecoverable energy and also strain energy, whichis recoverable. Formation of cracks and also fracture zones , friction, dampingand etc. are the main source of the irrecoverable energy. When there is vibrationin the concrete structure, then part of the strain energy is then re-transmitted as



kinetic energy back to the concrete structure, as indicated in the figure by brokenlines.

Besides the energy criterion, most design specifications for structuresunder impact loading specify the impact load-time function as the design impactload. Figure 2 shows the idealized design impact load for impact of Phantomfighter aircraft into concrete nuclear reactors at a speed of 215km/sec[3]. Thisdesign impact load is used for design of certain concrete nuclear reactors inGermany. In such a case, an impact load criterion must be applied for design ofthe structure. Therefore, a dynamic design method, based on both the energy andload criteria, is proposed here. Figure 3 shows the proposed design method forconcrete structures.

Energy nottransmitted into

concrete structure

Energy transmitted intoconcrete structure

We

Abscene

\A

>Irrecov

eneV

rbedrgyfa^f

^

***

erablergy/i

v

^

^

KineticenergyWk

"•

^

A

StrainenergyWs

Figure 1: Energy transformation process of impact collision

12,500

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07TIME IN SECONDS

Figure 2: Aircraft impact loading function



[Outline of type of structure (1) ]

is designimpact loadspecified? (2)

Yes

No

I Preliminary study & survey of possible impact collisions (3) |y '

I Determination of design impact conditions (4)|

Results of design forstatic loads (8)

I Selection of type of structure (7)|

]Setting of structural dimensions (9) \ '

| Dynamic structural analysis (10)]

No Is failurecondition

exceeded? (12)Is energy cntenonsatisfied? (11)

Yes

Figure 3: Flow of dynamic design method for structures under impact load

Bold lines in the flow chart indicate the safety provision according toenergy criterion while the broken lines indicate safety provisions according toload criterion. The flow of the proposed design method can be explained asfollows, where the numbers indicated correspond to the sequence of numberingin the flow:(l)Outline of type of structure - The type of structure to be designed is selected,

i.e., concrete handrail, concrete pier, etc.



(2)Is design impact load specified? - If the design impact load is specified for theparticular case, then further considerations regarding the impact load is notnecessary. If the design impact load is not specified, then considerations ofthe type and characteristics of the impact load function must be predictedbased on a numerical or empirical procedure.

(3)Preliminary study and survey of possible impact collisions - The type ofimpacting body that could possibly impact on the structure and also thepossible collision speeds and also collision angles have to be surveyed.

(4)Determination of design impact conditions - Based on the results obtainedfrom the survey in Step (3), the design impact conditions (type of impactingbody, collision angle, collision speed, etc.) are selected based on statisticalconsiderations.

(5)Is safety factor required? - It is considered that the safety factor can becalculated by applying the energy criterion. In the case of load criterion ,only a straight-forward procedure is possible, where the structure is checkedfor failure under the specified impact load condition.

(6)Calculation of design impact load - The impact design load is predicted basedon numerical models. In this dissertation, application of the multi-massmodel is proposed for predicting the design impact load function.

(T)Selection of type of structure - Further details of the concrete structure isselected. By considering the magnitude of the specified design impact load orspecified design impact collision, a structure that can effectively withstandthe impact collision is selected, i.e., reinforced concrte structure orprestressed concrete structure, simple supports or fixed supports, etc.

(S)Results of design for static loads - At present, most structures are notdesigned specifically for impact loading conditions. The structure is usuallydesigned to withstand the necessary design loads, such as dead load, liveload, earthquake load, etc. Once the dimensions of the structure have beendetermined based on the specified static design codes to withstand the normalloading conditions, the impact loading condition is then applied to thestructure.

(9)Setting of structural dimensions - If design of the structure to resist normalloading conditions in Step (8) has been performed, then the structuraldimensions are fixed. But if no preliminary design under normal staticloading conditions have been performed, then the structural dimensions areselected.

(lO)Dynamic structural analysis - Dynamic structural analysis is then performedbased on the specified design impact load or design impact condition. In thecontext of this dissertation, the dynamic nonlinear finite element analysisproposed in earlier paper[6] is applied. The "linked" procedure!?] is appliedfor the safety provision by energy criterion while the normal finite elementprocedure is applied for the safety provision by load criterion.

(1 l)Is energy criterion satisfied? - Safety provision based on the energy criterionis applied. Details are given in the following section.

(12)Is failure condition exceeded? - Safety provision based on the load criterionis applied. Details are given in the following section.

3.1 Safety Provision according to Energy CriterionThe safety factor for design of concrete structures under impact loads can bedetermined by applying the energy criterion. In the present limit state design forconcrete structures under static loads, the safety provision is determined by theratio of design ultimate setional forces and sectional forces during loading byspecified loads. When designing concrete structures subjected to impact loads,



the structure should be designed to act as a solid rigid body under impact loadswith a high occurrence frequency, but for impact loads that are not likely tooccur, the structure should deform and absorb part of the kinetic energy. Theenergy transmitted into a concrete structure during soft impact collisions can beassumed as,

Energy transmitted into concrete structure ( E }= (Kinetic energy in impacting body before impact collision)- (Energy dispersed in the impacting body by plastic deformation)- (Kinetic energy in impacting body at time of separation from

concrete structure)- (Energy lost : sound, friction, etc.) (1)

If the concrete structure is capable of absorbing all of the energytransmitted during the impact collision, then the structure would be intact andstructural failure would not occur. But if the structure is not capable of absorbingall of the energy transmitted during impact collision, then structural failure islikely to occur. Consequently, structural modifications, such as changes todimensions of the structure, amount of reinforcement, material parameters, etc.have to be carried out.

The safety provision for the energy criterion can be performed bycalculating the ultimate absorption energy ( E\ If the ultimate absorption energyis larger than the energy transmitted into structure ( E), then failure will notoccur in the particular structure. It is considered that the ultimate absorptionenergy of a structure is dependent of the loading rate of the load function [4, 5].Therefore, the loading rate for the design impact condition has to be evaluatedand the corresponding ultimate absorption energy must be calculated.

Figure 4 shows the definitions of calculations of energy absorbed bystructure and ultimate absorption energy. If the structure does not fail under thespecified design impact loads, then the energy absorbed ( E J is taken as the areaenclosed by the impact force function and the midspan deflection axis, atmaximum deflection. The amount of energy absorbable by a structure is relatedto the deformations, therefore the maximum deflection is selected. The amountof impulse transmitted during the impact collision at maximum deflection isreferred to as / in the context of this dissertation. For the similar loading rate,i.e., v =v , dynamic analysis is performed until failure in the concrete structure,as indicated in the figure. The final amount of energy absorbed is called theultimate absorption energy, E , while the corresponding amount of impulse atultimate failure is indicated by / . Since the impact failure mode is similar for thesame loading rate, the final failure conditions for both analyses would berelatively similar.

The safety factor for the concrete structure could then be expressed as,

EfuI Ef x /

Safety factor for impact loading, y = -jf- - -f^ — -^ (2)' ~£L A * "

If the safety factor is larger than unity, then the structure would not fa il.Concepts of failure energy in relation with loading rate is illustrated in Figure 5.Under a low loading rate, the bending failure mode is dominant but as theloading rate is increased, then the punching shear failure mode would be moreprominent. Therefore the envelope for failure energy of concrete structures


198 Structures Under Shock Ami Impact

INPUT OUTPUT

Deflection (6)

Deflection (<J)

Ie : Impulse at maximum deflectionIu : Impulse at ultimate failureEfe : Energy absorbed by structure at maximum deflectionEfu : Ultimate absorption energy

Figure 4: Calculation of energy absorbed by structure and ultimate absorption energy

Failure energy (Ef)

A

EKPS')

VLl VL2 VL4 Loading rate (vQ

: Failure envelope for impact toads- min { EKB) , EKPS)}--> EKB') :Structural modifications

EKPS) --> EKPS') : Structural mod (f (cations

Figure 5: Concept of failure energy under impact load



under different loading rates may be assumed as,

(3)

where, E(B) : Failure energy for bending failure mode,E/PS) : Failure energy for punching shear failure mode.

During the design of concrete structures according to the energy criteria inFigure 5, the following conditions would apply:l)Design criteria ( E^ v^) - No failure in structure. Dominant deformation mode

is bending.2)Design criteria (E^ v^) ~ Failure in structure by bending. Structural

modifications are necessary to improve the failure energy for bending failuremodetoE^B').3)Design criteria ( E^ v ) - No failure in structure. Dominant deformation mode

is shear. If shear failure should be prevented at all risk, structural modificationsshould be performed by improving the failure energy for punching shear failuremodetoEiPS').4)Design criteria (E^ v^) - Failure in structure by punching shear. Structural

modifications are necessary. If the failure mode is not important, thenimprovements to level E(PS') would be adequate. Or else improvements to levelE(B') would be necessary.

The flow of safety provision according to energy criterion is shown inFigure 6. The flow can be explained as follows:(13)Safety provision according to energy criterion - Start of safety consideration.(14)Setting of limit states - The limit states for design of the structure is

determined.(15)Is safety factor > 1.0? - The safety factor is considered based on Eq.(2).(16)Is failure mode important? - If the resultant impact failure mode is not a

limit state specified, then the design procedure will end at this stage,(17)Determination of impact failure mode - The failure mode is determined

based on results of the dynamic analysis.( 18)Possibility of punching shear failure? - This corresponds to E(PS) > E(B) in

Figure 5. If punching shear failure is not likely, then the design ends at thisstage.

(19)StructuraI modifications based on index of impact resistance - Modificationssuch as amount of steel reinforcement, structural dimensions, materialcharacteristics, etc. are performed based on evaluations of impact resistancepropertiesfll].

3.2 Safety Provision according to Load CriterionThe safety provision according to load criterion is relatively simple, incomparison to the energy criterion. The safety factor is not considered in thiscase. The flow of safety provision according to load criterion is shown in Figure7. The flow is as follows:(20)Safety provision according to load criterion - Start of safety consideration.

The design impact load is applied when specified.(21)Setting of limit states - The limit states for design of the structure is

determined,(22) A re the limit states exceeded? - A check on whether the limit states have

been exceeded is performed based on dynamic analysis results.



[Safety provision according to energy criterion (13)|

Structural modificationsbased on index of

impact resistance (19)

[Setting of limit states (14)|

Is safety factor > 1.07(15)

Safety factor I.

Is impact failure modeImportant? (16)

| Determination of Impact failure mode (17)]

Possibility of punchingshear failure? (18)

Figure 6: Flow of safety provision according to energy criterion

(23)Structural modifications based on index of impact resistance - Modificationssuch as amount of steel reinforcement, structural dimensions, materialcharacteristics, etc. are performed based on evaluations of impact resistanceproperties.

4. Case Study of Design of Reinforced Concrte Handrail

As a case study of the dynamic design procedure proposed, the design ofreinforced concrete handrail (guardrail) under vehicular impact is discussed. Thenumbers in brackets indicated below are in relation to the numbers in the flow ofthe design procedure indicated in Figures 3, 6, and 7. The case study is asfollows:(l)Outline of type of structure - Concrete handrail.(2)ls design impact load specified? - No.(3)Preliminary study & survey of possible impact collisions - Vehicular

collisions are considered.



(4)Determination of design impact collision - The design impact collision isselected as in Figure 8. It simulates a medium sized car colliding at arelatively low speed. For convenience, the angle of collision is set at 90degrees (perpendicular to handrail).

(5)1 s safety factor required? - Yes.(T)Selection of type of structure - Reinforced concrete, fixed cantilever at bottom

of handrail.(S)Results of design for static loads - A normal concrete handrail is selected.(9)Setting of structural dimensions - The dimensions and model according to the

layered finite element procedure are shown in Figures 9(a) and 9(b),respectively.

(lO)Dynamic structural analysis - The linked procedure in Reference 7 isapplied. The main results are given in Table 2, Figures 10, 11 and 12. Theresults for this case is referred to as "Case 1" in the Table and Figures.

(ll)Is energy criterion satisfied? - Failure by concrete crushing at rear face isindicated in the analysis (refer Table 2). Proceed to Step (9).

(9')Setting of structural dimensions - The amount of steel reinforcement in the

Safety provision according to load criterion[Design impact load] (20)

Structural modificationsbased on index of

impact resistance (23) | Setting of limit states (21) |

Figure 7: Flow of safety provision according to load criterion

v=7.5m/sec (27km/hr)

RC handrail

VVO.etf W,=0.3tf

- Reinforcement ki=^=kg=2tf/cm

Collision angle = 90°

Figure 8 Setting of design impact condition of RC handrail



longitudinal direction of front face (tension side) is increased from 15cmpitch to 10cm pitch because failure by concrete in compression occurred atthe rear face. Details of the cross sectional areas are indicated in Table 3.The analysis is now referred to as Case 2.

(lO')Dynamic structural analysis - The results are indicated in Table 2, Figures10, Hand 13 as Case 2. . .

(11 ')Is energy criterion satisfied? - Failure by concrete crushing at front lace isindicated in the analysis (refer Table 2). Proceed to Step (9).

(9")Setting of structural dimensions - The amount of steel reinforcement in thelongitudinal direction of rear face (compression side) is increased from 15cmpitch to 10cm pitch because of concrete crushing in the front face. Details ofthe cross sectional areas are indicated in Table 3. The analysis is nowreferred to as Case 3.

250

8

r-10

X

(Detail of handrail)

x." :_ . ,_ --

(unit : mm)

(a) Details of RC handrail

C.L.Concrete layer

A

c

Y

A

•X

^XX

'; 's@'l 00=800

-D

4(a) 150=600

2000

3(0)200=600

C ;Ar-T C% :

\Reinfo

i /— j: CXo

; o, / II/ 0; O; %j OT \'4 in)

rceme

i i

NO

'_ ^

ntlc

k

/

ayer

C.L (Plan) (Unit: mm) (Section D-D)

(b) Layered finite element meshes for RC handrail(l/2 portion)

Figure 9: Dimensions and model of RC handrail



(10")Dynamic structural analysis - The results are indicated in Table 2, Figures10, 11, 14 and 15 as Case 3.

(1 OIs energy criterion satisfied? - No failure in structure. Proceed to Step (13).(13)Safety provision according to energy criterion - Proceed to Step (14).(14)Setting of limit states - Structural failure by bending mode to prevent

concrete scabbing.(15)Is safety factor > 1.0 - Safety factor is calculated. The ultimate absorption

energy is calculated by the finite element method and the results areindicated in Table 2 as " Ultimate". The safety factor is calculated based onresults in Table 2 as;

Table 2: Main results of dynamic analysis for design of RC handrail

Case

123

Ultimate

Case

123

Ultimate

Loadingrate

(tf/msec)4.204.344.144.14

Load atfailure(tf)30.8630.81

(30.86)*43.08

Index of localdeformation(x lO /cm )

10.229.331.807.55

Deflectionat failure(mm)3.101.15

(0.50)**1.41

Impulse

(kgf-sec)151.1143.4123.5224.0

Crackingload(tf)

21.6222.3323.2425.70

Totalenergy(kgf-cm)103002960

1020****5540

Concreteplasticity load

(tf)***30.1230.60

40.20

Failure

mode*****PSPS

(B)******B

Reinforcementyielding load

(tf)30.230.6

40.4

Failure condition

Concrete crushing at rear faceConcrete crushing at front face

Concrete crushing at front face

* Maximum impact load** Maximum deflection

*** Plasticity in compression****Total energy at maximum deflection***** B: Bending, PS: Punching shear***** Main deformation mode

(Center of handrail)(Side end of handrail)

Figure 10: Distribution of transverse deflection at failure(Case 1, 2, 3)



(Top of handrail)

(Bottom of handrail) * 1 ' ' '0 1 2 3 4

Deflection (mm)

Figure 11: Distribution of longitudinal deflection at failure(Case 1, 2, 3)

30-

S 20

oOJa

1 2 3Deflection (mm)

Figure 12: Impact force - central deflection relation for Case 1



1 2 3Deflection (mm)

Figure 13: Impact force - central deflection relation lor Case 2

Table 3: Structural modifications of RC handrail

\

©Case 1

®Case 2

®Case 3

Tension steel (2nd layer in Figure 9)LongitudinaldirectionA,(cm2)

16.471(13@D13)

25.340(20@D13)

25.340(20@D13)

TransversedirectionA,(cm2)

10.136(80D13)

10.136(8@D13)

10.136(8@D13)

Compression steel (7th layer in Figure 9)LongitudinaldirectionA,(cm2)

16.471(13OD13)

16.471(13@D13)

25.340(20OD13)

TransversedirectionA, (cm 2)

10.136(8@D13)

10.136(8GD13)

10.136(8@D13)

Safety factor, y . =

Efu^UltitimateE3 X I Ultimate

5540 x 123.51020x224.0

= 2.99(> 1.0)

Proceed to Step (16).(16)ls impact failure mode important? - Yes.(17)Determination of impact failure mode - Bending failure mode is indicated in



the results in Table 2. Proceed to Step (18).(IS)Possibility of punching shear failure - No.

The design of the concrete handrail ends at this stage with the dimensionsused in "Case 3" being selected, with a safety factor of 2.99.

c0.8-

L

&0.6-L

oo 0.4

2 0.2

i=1075mm\

_h=775mm

• • •.. ^~ -^

h=675mrri"

h: height from bottomof handrail

(Center of handrail)(Side end of handrail)

Figure 14: Distribution of transverse deflection at failure(Case 3)

30-

120-

CT3Q.

10--

0.2 0.4Deflection (mm)

0.6

Figure 15: Impact force - central deflection relation for Case 3


Structures Under Shock Ami Impact 207

5. Conclusions

In this paper, a dynamic design procedure for concrete structures subjected toimpact loads is proposed, based on the energy criterion and the load criterion.And also, a case study for designing a reinforced concrete handrail under impactcollision from a light vehicle is illustrated.

The main results of this paper can be summarized as follows;(l)Limit states for different types of structures under different impact loading

conditions are necessary. Designing a structure according to the ultimate limitstates would produce a more rational design result. When designing concretestructures under impact loading, the allowable failure modes should also bespecified.

(2)A dynamic design procedure that is capable of considering the impact failuremodes and also the safety factor is proposed based on an energy criterion.Furthermore, to allow application of specified design impact loads in design,a load criterion is also proposed. For safety provision by the energy criterion,the safety factor is taken as a ratio between the ultimate absorption energyand the energy absorbed by the structure under the specified design impactconditions. The design procedure would allow a rational and effective designof reinforced concrete structures to be performed.

(3)A case study of design of reinforced concrete handrail for vehicle impactconditions is performed to point out the applicability of the proposed designprocedure. The results indicate that the proposed design procedure can bepractically applied on full scale structures.

References

1. Miyamoto, A., Ishibashi, T. & Mito, M. Non-Linear Dynamic Analysis andDesign Concepts for RC Beams under Impulsive Loads, JSCE Journal ofStructural Engineering, 1994, 40A, 1605-1618.2. Koyanagi, W., Rokugo, T. & Horiguchi, H. Failure Condition of Steel FiberReinforced Concrete Beam Element under Repeated Impact Loading,Transactions of the Japan Cement Association, 1984, 38,381-384.3. Kamil, H., Krutzik, N., Kost, G. & Sharpe, R. An Overview of Major Aspectsof the Aircraft Impact Problem, Nuclear Engineering and Design, 1978, 46, 109-121.4. King, M. W., Miyamoto, A. & Nishimura, A. Failure Criteria and Analysis ofFailure Modes for Concrete Slabs Under Impulsive Loads, Memoirs of theGraduate School of Science and Technology, Kobe University, 1991, 9-A, 1-40.5. Miyamoto, A., King, M. W. & Fujii, M. Analysis of Failure Modes forReinforced Concrete Slabs Under Impulsive Loads, Journal of the AmericanConcrete Institute, 1991, 88, 5,538-545.6. Miyamoto, A. & King, M. W. Concrete Structures under Soft Impact Loads,Chapter 5, Shock and Impact on Structures, eds Brebbia, C. A. & Sanchez-Galves, V., pp. 107-204, Computational Mechanics Publications, Southampton,UK & Boston, USA, 1994.7. Miyamoto, A., King, M. W. & Fujii, M. Integrated Analytical Procedure forConcrete Slabs under Impact Loads, ASCE Journal of Structural Engineering,1994, 120,6, 1685-1702.


process. since impact loading on concrete …...design concept for reinforced concrete slab...

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