Reinforced Concrete in Blast-Hardened Structures - ACS Symposium

Chapter 5

Reinforced Concrete in Blast-Hardened Structures James E. Tancreto

Downloaded by NANYANG TECHNOLOGICAL UNIV on October 13, 2017 | http://pubs.acs.org Publication Date: July 20, 1987 | doi: 10.1021/bk-1987-0345.ch005

Naval Civil Engineering Laboratory, Port Hueneme, CA 93043

The design criteria for reinforced concrete is being revised as the result of dynamic tests that show improved response to explosive loads. The improved design criteria will result in safer and less expensive protective shelters and barriers. Improvements in the design criteria are mainly the result of increases in the allowable design stresses and allowable ultimate flexural deflections under shock loads. Conventionally reinforced concrete, with the proper design considerations, may now be designed for up to four times the deflections (and energy absorbing capacity) allowed by the old criteria. The improved response criteria for conventional reinforced concrete will reduce the need for more expensive laced reinforced concrete. A summary of the new design criteria is presented with emphasis on the important changes to the flexural design criteria. Explosive storage and operating f a c i l i t i e s must be designed to protect personnel, equipment, and contents from the effects of an accidental explosion. Hardened structures can be c l a s s i f i e d as shelters or b a r r i e r s . Shelters are designed to completely shelter t h e i r contents from the blast and fragments produced by an explosion. Barriers are walls or open structures that provide p a r t i a l protection. Barriers are usually designed to prevent sympathetic detonation of explosives by stopping fragments and reducing blast pressures from an adjacent explosion. Reinforced concrete i s the most commonly used construction material for structures designed to r e s i s t explosive blast loads. It i s used extensively i n blast hardened structures because of i t s strength, d u c t i l i t y (when properly designed), mass, penetration resistance, r e l a t i v e economy, and universal a v a i l a b i l i t y . I t s strength, mass, and d u c t i l i t y provide high resistance to the extreme blast pressure (psi) and impulse (psi-ms) loads. It i s important to remember that (unlike i n s t a t i c load design) i n the

This chapter not subject to US. copyright Published 1987 American Chemical Society

Scott and Doemeny; Design Considerations for Toxic Chemical and Explosives Facilities ACS Symposium Series; American Chemical Society: Washington, DC, 1987.


5. TANCRETO

Reinforced Concrete in Blast-Hardened Structures

93

design for dynamic loads, the mass and d u c t i l i t y of the element are as important as i t s strength. The mass and strength also provide excellent fragment and debris penetration resistance. Unhardened reinforced concrete, designed for normal (non-explosive) loads w i l l generally be much more blast resistant than other s t r u c t u r a l materials because of these attributes. Blast hardened reinforced concrete structures may s t i l l be very massive and expensive. The expense increases when lacing reinforcement i s necessary to provide d u c t i l i t y at the large deflctions caused by severe blast loads. Tests have shown that conventional reinforced concrete (without lacing) can attain much larger deflections, with proper design, than are being allowed by existing c r i t e r i a . New c r i t e r i a are being developed to r e f l e c t these test r e s u l t s . A summary of the new evolving c r i t e r i a , especially the bending c r i t e r i a as reflected i n the t r i - s e r v i c e design manual, TM 5-1300/NAVFAC P-397/AFM 88-22, "Structures to Resist the Effects of Accidental Explosions", i s presented here. Behavior Modes Two modes of behavior, d u c t i l e and b r i t t l e , must be considered i n the design of hardened reinforced concrete structures. Reinforced con crete can behave with great d u c t i l i t y during the f l e x u r a l response of bending members (slabs, beams, girders, e t c . ) . This d u c t i l e f l e x u r a l mode results i n large deflections that can absorb the high energy from the blast loads. The b r i t t l e modes (shear f a i l u r e , compression f a i l u r e , s p e l l i n g , breeching, and fragment penetration) may reach f a i l u r e under r e l a t i v e l y low energy input levels or at small deflections due to load concentrations and low ductility. B r i t t l e f a i l u r e s occur before s i g n i f i c a n t bending deflection can develop. Reinforced concrete bending elements are designed to r e s i s t the blast loads i n the high energy absorbing f l e x u r a l mode and then shear reinforcement i s provided to prevent an early shear f a i l u r e . A basic design requirement f o r reinforced concrete i s that f l e x u r a l elements be designed so that f a i l u r e i s forced to occur i n bending and not shear. Ductile Behavior. When a reinforced concrete element i s loaded by the blast load i t deflects e l a s t i c a l l y u n t i l p l a s t i c y i e l d i n g occurs along highly stressed y i e l d l i n e s . I t then deflects plas t i c a l l y (with a small increase i n resistance from s t r a i n hardening of the steel) to i t s maximum deflection. Figure 1 shows a t y p i c a l resistance d e f l e c t i o n curve. The degree of d u c t i l i t y i s repre sented by the maximum support rotation (and center deflection) that can be attained without f a i l u r e . Figure 2 shows the relationship between support rotation and maximum deflection of a one-way bending member. The relationship f o r a one-way element i s : X = (L/2) tan θ where

X = deflection (at center span of one-way member) θ β angle of rotation at support


TOXIC CHEMICAL AND EXPLOSIVES FACILITIES


94

- Yield Failure of compression concrete Beginning of strain hardening

Tensilf "V- Tensile

^

^ *du

membrane resistance

x(0= 12°) No shear reinf.

Ε ©

Single leg stirrups - N o shear reinf. -Lacing-

Figure 1.

Typical resistance-deflection curve f o r f l e x u r a l response of concrete elements.



TANCRETO

Figure 2.


Deflection of a one-way simply supported bending element.



96

TOXC I CHEMC IAL AND EXPLOSV IES FACILITIES

The relationship f o r two-way elements (such as slabs supported on three or four sides) i s more complicated. An approximate r e l a t i o n ship can be obtained f o r any element by substituting the short span for L/2 i n the above equation. The allowable rotation and deflec t i o n i s strongly dependent on compression and buckling strength of the reinforcement on the compression side of the element. Previous c r i t e r i a have allowed a design support rotation, Θ, of 2 degrees for conventionally reinforced concrete. When lacing s t e e l (as shown i n Figure 3a) i s used to prevent buckling of the compression reinforcement and to contain the cracked concrete, a design support rotation of 12 degrees i s allowed. Testing has shown that conventionally reinforced concrete (without lacing) can safely sustain much larger support rotations than 2 degrees. The new c r i t e r i a are taking advantage of these test results to allow increased support rotations and center deflections. The changes include allowable support rotations of 4 degrees for conventionally reinforced concrete (with single leg s t i r r u p s , as shown i n Figure 3b, to increase d u c t i l i t y ) and 8 degrees for reinforced concrete that can develop t e n s i l e membrane resistance. Tensile membrane resistance can be counted on i n most two-way slabs and f l a t slabs (even when they are simply supported). Shear s t e e l i s not required f o r d u c t i l i t y i n a t e n s i l e membrane slab but may be necessary f o r shear resistance. These increased allowable support rotations result i n increased allowable deflec tions of two and four times the o l d c r i t e r i a deflections. The area under the resistance d e f l e c t i o n curve (see Figure 1) between X = 0 and X = X i s representative of the energy absorbing capacity of the structure. Thus, increasing the allowable design d e f l e c t i o n proportionally increases the area under the resistance-deflection curve. Figure 4 shows the design e l a s t o - p l a s t i c and p e r f e c t l y p l a s t i c (for support rotations > 5 degrees) resistance-deflection functions. The increased impulse capacity of a structure i s proportional to the square root of the increase i n the area under the r e s i s tance-deflection curve. The effect of mass can be e a s i l y shown with the following equation f o r the impulse capacity of a d u c t i l e element with large allowable d e f l e c t i o n and a p e r f e c t l y p l a s t i c resistance function (as shown i n Figure 4b). —

2 m r Χ u u m

i = blast load impulse, psi-ms 1/3 m = e f f e c t i v e unit mass i n ultimate range, psi-ms/lb u r = ultimate unit resistance, p s i u X = maximum d e f l e c t i o n , i n m In the equation above, mass carries the same "weight" as strength and d u c t i l i t y (deflection) i n developing impulse capacity. The allowable support rotation and d e f l e c t i o n f o r laced r e i n forced concrete has remained at 12 degrees. The increased allow able deflections for conventionally reinforced concrete w i l l reduce


TANCRETO



Single leg stirrups

m— .· *· \ * ·* ·*» *·.

la-- '

•.;||·:.;

'n • Flexural reinforcement b. Single leg stirrups.

A.

Figure 3.

Lacing reinforcement.

Typical shear reinforcement.



98


Deflection, in. a. Elasto-plastic resistance-deflection (any 0).

Deflection, in. b. Perfect plastic resistance-deflection ( 0 > 5 ° ) .

Figure 4.

Typical design resistance-deflection

functions.


5.

TANCRETO



the need f o r expensive structures.

laced

reinforced

concrete

99

i n hardened

B r i t t l e Behavior. Three related b r i t t l e modes of f a i l u r e create concrete fragments during bending response: s p e l l i n g , scabbing and p o s t - f a i l u r e fragmentation. Spalling and scabbing consist of concrete debris from the concrete cover over the f l e x u r a l reinforcement. Spalling occurs before s i g n i f i c a n t bending can begin and i s caused by high t e n s i l e forces created by the blast pressures. Scabbing, a form of s p a l l i n g , occurs at large bending deflections when severe cracking of the concrete cover has occured. Postf a i l u r e concrete debris are created from the collapse of an element and are usually numerous, large and have r e l a t i v e l y high v e l o c i t i e s . Spalling and scabbing can be hazardous to personnel, sensit i v e equipment, and sensitive explosives. Spalling and scabbing can be controlled with s p a l l plates, and by l i m i t i n g design deflections. Postfailure fragments are avoided by designing to prevent f a i l u r e (the normal hardened structure design requirement). Other b r i t t l e f a i l u r e modes include shear (direct and diagonal tension), compression f a i l u r e , breeching, and fragment penetration. Bending elements must be designed to develop t h e i r f u l l bending capacity. Shear f a i l u r e s are controlled by providing reinforcement adequate to support the f u l l bending resistance ( r ) of the member. Compression f a i l u r e i s controlled with proper d i s t r i b u t i o n of the reinforcement (usually equal s t e e l percentages on the tension and compression sides) and, f o r design rotations above 2 degrees, l a t e r a l support of the compression reinforcement with single leg stirrups or lacing. Underreinforced sections are used i n design to keep the shear and compression stresses low, allowing d u c t i l e bending response to develop before shear or compression f a i l u r e can occur. A x i a l compression members (columns) are designed to provide adequate compression and shear strength to support the ultimate resistance of supported bending members. Breeching i s a l o c a l perforation of the concrete element by the extremely high blast pressures of a close explosion. High v e l o c i t y concrete fragments can r e s u l t . Breeching f a i l u r e s are controlled by providing adequate reinforcement, concrete thickness and standoff distance to the explosive. Reinforced concrete i s very resistant to fragment penetration and i s frequently used just for t h i s reason. Primary fragments can produce s p a l l i n g of the concrete. Perforation by metal fragments and concrete s p a l l i n g are controlled by providing adequate concrete thickness based on empirical relationships using fragment mass and velocity. Dynamic Strength of Materials The allowable strength of materials i s higher under dynamic loads, which produce high s t r a i n rates, than under s t a t i c loads. This results i n higher resistance to dynamic loads. The most important increases are i n the compression strength of concrete and the y i e l d strength of the s t e e l reinforcement.


100


S t a t i c Strength. ASTM A 615, Grade 60 reinforcement, i s recommended for hardened reinforced concrete design. The average y i e l d strength for this s t e e l i s 10 percent greater than the minimum required ASTM value (60,000 p s i ) , while the ultimate strength i s not much greater than the ASTM minimum. The recommended s t a t i c y i e l d and s t a t i c ultimate design strengths are:


f

y

= 66,000 p s i

and

= 90,000 p s i

In the design calculations for f l e x u r a l elements, the concrete strength i s only important i n determining the shear resistance of elements undergoing less than 2 degrees support rotation. However, stronger concrete w i l l also result i n less cracking and crushing of concrete between the reinforcement at large rotations. It i s recommended that the design concrete s t a t i c design strength be 4000 p s i , and never less than 3000 p s i . Dynamic Strength. The dynamic design strengths for s t e e l r e i n forcing and concrete are equal to t h e i r s t a t i c design strengths times the appropriate Dynamic Increase Factor (DIF). (dynamic)

(static) 1

Table I summarizes the appropriate DIF s by type of stress.

Table I.

Dynamic Increase Factors (DIF) for Reinforced Concrete

Low-Intermediate (& High) Design Pressures* Type of Stress Bending Diag. Tension Direct Shear Bond Compression

Reinforcing Steel Yield 1.17 1.00 1.10 1.17 1.10

(1.23) (1.10) (1.23) (1.13)

Ultimate 1.05 1.00 1.05

Concrete ultimate 1.19 1.00 1.10 1.00 1.12

(1.25)

(1.16)

*The revised Tri-Service design manual uses Far and Close-in Design Ranges rather than Low-Intermediate and High Design Pressures

Flexural Design Flexural member design requires the determination of: (1) the design blast loads, (2) the i n i t i a l design cross-section, (3) an idealized resistance deflection function, (4) the calculated response (maximum deflection) and, (5) allowable ultimate deflect i o n and (6) design for shear.



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101

Blast Loads. The f l e x u r a l member Is designed for the expected blast overpressure loads (pressure and impulse). External blast overpressure loads are primarily dependent on the equivalent explosive weight (W), the range from the structure (R), and the orientation of the structure to the shock wave. The design loads include the effect of a 20% factor of safety on the explosive weight (Design Explosive Weight = 1.2W). Other factors, including charge shape, the height of burst (HOB), t e r r a i n e f f e c t s , and casing thickness, can influence the blast overpressure and impulse loads and are included i n the loads determination when possible. The loads from external near-surface burst explosions are based on hemispherical surface burst relationships. Peak pressure (P p s i ) and plotted vs. scaled distance (R/W f t / l b ' ). Roof and sidewall elements, side-on to the shock wave, see side-on loads (P and i ). The s s front wall, perpendicular to the shock wave, sees the much higher r e f l e c t e d shock wave loads (P and i ). An approximate triangular pressure-time relationship i sshown i n Figure 5a. The duration, T, is determined from the peak pressure and impulse by assuming a t r i angular load. Complete load calculations include dynamic loads on side-on elements, the effect of clearing times on reflected pressure durations, and load variations on s t r u c t u r a l elements due to t h e i r size and varying distance from the explosive source. Internal explosive loads include d i r e c t r e f l e c t e d shock pressures plus (1) the reflected shock pressures from adjacent surfaces and (2) internal gas pressures from the gaseous products of the explosion. The peak gas pressure, which i s a function of the charge density (charge weight to structure volume r a t i o , tf/V), i s r e l a t i v e l y low but can be of long duration with large impulse. Frangible surfaces are commonly used to quickly vent the gas pressures and reduce the internal design load on the hardened structure. The d i r e c t plus reflected internal shock pressures and the gas pressures can be determined from curves i n NAVFAC P-397. A b i l i n e a r load function i s obtained by merging the shock pressure and gas pressure curves as shown i n Figure 5b. T r i a l Cross-Section. A t r i a l cross-section i s chosen that includes the concrete thickness, and the tension and compression s t e e l percentages ( i n the horizontal and v e r t i c a l directions for a two-way slab). The optimum d i s t r i b u t i o n of horizontal and v e r t i c a l s t e e l i s obtained when 45 degree y i e l d lines are obtained i n a y i e l d - l i n e analysis for ultimate resistance. The minimum s t e e l percentage, either way and i n tension or compression, i s 0.15%. The optimum t o t a l positive or negative reinforcement r a t i o (p^ + p ) has been found to be between 0.6% and 0.8%. A value i n t h i s range should be used for design. r

v

Resistance-Deflection Function. The resistance-deflection function establishes the dynamic resistance of the t r i a l cross-section. Figure 4a shows a t y p i c a l design resistance-deflection function with e l a s t i c s t i f f n e s s , Kg ( p s i / i n ) , e l a s t i c d e f l e c t i o n l i m i t , (in) and ultimate resistance, r ( p s i ) . The s t i f f n e s s i s determined from a s t a t i c e l a s t i c analysis using the average moment of i n e r t i a of a cracked and uncracked cross-section. (For design n



102


Elapsed Time, t (msec) a. Typical external design load function.

P-|

=

peak shock overpressure, psi

?2

-

peak gas overpressure, psi

T^

=

duration of design shock load, msec

Τ2

~

duration of design gas load, msec

ij

=

shock inpulse,psi-msec

i2

=

gas impulse, psi-msec

τ,

T

2

Elapsed Time, t (msec) b. Typical internal design load function.

Figure 5.

Design overpressure versus time.



5.

TANCRETO


103

deflections > 5 degrees, the p e r f e c t - p l a s t i c resistance-deflection function i n Figure 4b may be used. This eliminates the need f o r determining the s t i f f n e s s of the element.) Ultimate resistance i s determined s t a t i c a l l y using y i e l d - l i n e analysis and dynamic stress allowables. The ultimate resistance i s the uniform s t a t i c pressure that the element can support when y i e l d i n g begins at Xg. The ultimate resistance depends on the moment resistance of the crosssection, the geometry of the element, and the support conditions. The moment resistance of the section changes with increasing deflection as the concrete cover crushes (reducing the moment capacity s l i g h t l y ) and as the s t e e l reinforcement strain-hardens and increases i n strength from y i e l d to ultimate (increasing moment capacity). These variations are averaged, depending on the design deflection, to obtain the straight l i n e design resistance functions shown i n Figure 4. Maximum Deflection. The response of the t r i a l section i s deter mined from an equivalent single-degree-of-freedom (SDOF) springmass system. Response charts are available f o r the triangular or b i l i n e a r load functions (see Figure 5) and an e l a s t i c p l a s t i c resistance function (see Figure 4). The response charts give X /X^ versus P/r and T/T^. Β and Τ are the peak pressure and duration, respectiveYy, i n the load function. T^ i s the natural period of the equivalent SDOF spring-mass system. The natural period i s given by:

where

= SDOF load-mass factor The load-mass factor, K^, transforms the actual dynamic system to the equivalent SDOF system. The value i s usually between 2/3 and 3/4 and depends on the geometry, end conditions, support conditions, and range of behavior ( i . e . e l a s t i c , e l a s t o - p l a s t i c , or plastic). The maximum d e f l e c t i o n , X , i s then compared to the allowable ultimate d e f l e c t i o n to determine the adequacy of the t r i a l section. Allowable Deflection. The allowable d e f l e c t i o n i s d i r e c t l y c a l culated from the allowable support rotation and the shortest distance from a support to a y i e l d - l i n e (L/2 f o r a one-way ele ment). The allowable support rotation depends on the d u c t i l i t y of the section as summarized i n Table I I . Tensile membrane behavior requires continuous reinforcement s t e e l to support in-plane stesses. Two-way slabs and f l a t slabs, with fixed or simple supports, can usually s a t i s f y the requirements for t e n s i l e membrane resistance. Design with t e n s i l e membrane resistance i s the same as f o r f l e x u r a l resistance since the moment capacity of the section i s used to determine ultimate resistance. Tensile membrane resistance at 8 degree rotation must be at least


104


equal to the bending resistance to insure that adequate strength i s available when bending resistance i s lost.


Table I I . Allowable Support Rotations, θ ' u

Shear Reinforcement

θ * u

Tensile Membrane Resistance

(deg)

No No Yes No

2 4 8 12

None** Stirrups None** Lacing

*Does not apply i f containment i s required. **Not required for d u c t i l i t y but must be used i f required for shear.

If the maximum deflection calculated for the t r i a l section i s less than the allowable deflection, then the section i s adequate i n bending and the shear stresses must be checked. Shear Design. The shear loads, V , are based on the ultimate bending resistance, r , of the structural element. Shear resistance i s provided to support the resulting shear stresses, ν . This allows the element to reach i t s f u l l dynamic f l e x u r a l loa

Reinforced Concrete in Blast-Hardened Structures - ACS Symposium

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