MC STEELSER (Almacén Industrial Piura 1056 Con Juntas - Dramix 3D6550 BL 1520)

Dramix®

Dramix® ProCopyright© NV BEKAERT SABekaertstraat 2, 8550 Zwevegem

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Design of ground supported steelfiber reinforced floors based on the Losberg Yield Line model

Design made for : STEELSER SACProject : Losa Industrial PiuraProject Segment : Losa 1056m2 Con Juntas

Design made by : Giomar MoyaStreet : Av. Néstor Gambetta 6429Address : CALLAO CALLAO 6Tel. : +5116136666Fax : +5116289506Email : [email protected]

Introduction• Design guidelines

Dramix® steelfibers cause a change in material properties and the main effect of adding steelfibers to the concrete is to provide toughness to this brittle material.

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One of the major applications, for which Dramix® steelfibers are particularly suitable, is slabs-on-grade. Plain concrete slabs fail suddenly once it cracks while Dramix® steelfiber concrete is able to sustain higher loads after first cracking.It is therefor important that the correct design principles are being used which take the toughness (post-crack) behaviour into account.Elastic design methods, such as Westergaard, are not suitable, as they give no indication on the safety build into the floor by adding the steelfibers to the concrete.Therefor this design note is based on the yield line principles and consists out of three major parts:

ULTIMATE LIMIT STATE design

Laboratory testing of full-scale SFRC slabs-on-ground indicated that the slab behaves linear-elastically up to the proportional limit (FR). As the elastic limit is exceeded, the concrete remains ductile but the concrete modulus softens. This is illustrated in Figure 1 by the decreased slope of the curve between points FR and FR’. As the load is increased beyond FR’, the concrete modulus softens again. More redistribution of stresses and energy absorption occurs until the ultimate strength of the slab cross-section is reached. In the strength design procedure, the margin of safety is provided by dividing the calculated ultimate strength by a load factor ( Q) and a material factor ( fd).

The material properties, equivalent flexural stress, of the Dramix® steelfiber concrete should be tested according the JSCE-SF4 (Japan), ASTM C 1018 – 94b (U.S.A.), TR34 (U.K.), DBV –Merkblätter Faserbeton (Germany), CUR 35 (The Netherlands), NF P 18 – 409 (France), NBN B 15-238 (Belgium) or similar standards.

Important to mention is that the Post-Crack strength up to a deflection of mm (l = Span

between the supports of the test beam) has to be measured with a deformation steered test machine.

The first crack strength of the concrete is NOT a valid design value, as it gives no indication on the Post-Crack behaviour of the composite material.

SERVICEABILITY STATE checkIn the Serviceability State following items are checked.- Possible cracks opening in case the concrete does crack.For the crack opening design following loads are being considered

>> Unfactored external loads>> Stresses due to shrinkage.>>

top to bottom of the slab.

Deflection of the floor ( settlement of the sub-base)

Punching

Even as practice has shown that punching is very rarely the cause for slab failure this design note makes a check whether the highest point and/or wheelloads could cause punching failure.

•Construction Recommendations

Following topics represent some of the most important features of slab-on-ground construction. See industry guidelines such as TR345 and ACI 306 for more comprehensive guidelines. The following



items should be specified in the contract documents prepared by the engineer of record:

By no means do these construction recommendations replace the general contract specification or the experienced layman. 1. Specifications – Standard Specifications for Steel Fiber Reinforced Concrete are available through Bekaert Corporation.

2. Steel fiber type and dosage – While all Dramix® steel fibers for flooring applications have the same hooked-end configuration, the fiber type (length, diameter and tensile strength) varies depending on specific project conditions. It is important to provide the exact fiber designation and dosage on the contract documents.

3. Batching considerations – See Dramix® Product data sheets

4. Soil support system – The soil support system should be well drained and provide adequate and uniform load-bearing support. Specific attention should be given to the site preparation requirements, including proof-rolling, because the performance of a slab on ground depends on the integrity of boththe soil support system and the slab. The in-place density of the soil support system should be at least the minimum required by the specifications, and the base should be free of frost before the concrete placing begins and able to support construction traffic such as loaded truck mixers.

Proof-rolling is an excellent means to determine that the soil support system is adequate to provide a uniformly stable and adequate bearing support during and after construction. Proof-rolling, observed by the owner’s representative, should be accomplished by a loaded tandem axle dump truck, a load truck mixer, roller, or equivalent. In any case, multiple passes should be made using a pre-established grid pattern.

If rutting or pumping is evident at any time during the preparation of the soil support system, repairs such as, but not limited to, raking smooth or compacting with suitable compaction equipment should be undertaken. "Rutting" normally occurs when the surface of the base is wet and the underlying soils are firm. "Pumping" normally occurs when the surface of the base is dry and the underlying soils are wet. Any depression in the surface deeper than 13 mm should be repaired.

The tolerance of the subbase should follow the local standards or jobsite specification with a maximum tolerances of

+/- 10 mm for +/- 30 mm for Linear interpolation between 150 mm and 400 mm for corresponding maximum

tolerances.

5. Vapour retarder – Proper moisture protection is desirable for any slab on ground where the floor will be covered by tile, wood, carpet, impermeable floor coatings, (urethane, epoxy, or acrylic terrazzo), or where the floor will be in contact with any moisture-sensitive equipment or product. Many industrial warehouses or production facilities do not require a vapour retarder. It is suggested that vapour retarders should be installed only in conditions that warrant their use.

If a vapour retarder is required due to local conditions, it should be placed under a minimum of 75-mm to 100-mm granular fill such as "crusher run" material. Following compaction, the surface may be choked off with a fine-grade material to reduce friction between the base material and the slab. The granular fill, as well as the fine-graded material, should have sufficient moisture content to be compactible, but still be dry enough at the time of concrete placement to act as a "blotter."

6. Aggregates –Aggregates should conform to industry standards such as ASTM C 33. Combined aggregate gradations should conform to industry standards such as ACI 544.1R8. A uniform gradation is necessary to produce a desirable matrix while reducing water demand of the concrete mixture and reducing the amount of cement paste required to coat the aggregates and steel fibers.

7. Proportioning –Mix design proportions of SFRC are similar to those of conventional concrete mixes. Recommended ranges of mix proportions are provided in industry standards such as ACI 544.1R. For high dosage rates the mix design should be optimised in view of workability and pumpability.



8. Admixtures – Admixtures are commonly used with SFRC to improve workability and finishability. If more than one type of admixture is used, each should be batched separately. Admixtures should meet the requirements of local industry standards.

9. Curing –Curing is vital to good flatwork. Wet burlap, plastic film and sprayed-applied membranes may be considered as conditions warrant. Industry standards such as ACI 302 are available for more comprehensive information on curing.

10. Saw-cut joints –Both conventional wet-cut and early-entry dry-cut saws may be used to sawcut joints in SFRC floors. The saw-cut depth using conventional wet-cut blades should be 1/3 of the slab depth. The saw-cut using the early-entry saw should be 1/3 of the slab depth if practicable and a minimum of 25-mm.

Regardless of the process chosen, saw-cutting should be performed (1) before the concrete starts to cool, (2) as soon as the concrete surface is firm enough not to the torn or damaged by the blade, and (3) before random-drying-shrinkage cracks can form in the concrete slab. Shrinkage stresses start building up in the concrete as it sets and cools. If sawing is unduly delayed, the concrete can crack randomly before it is sawed.

• LiabilityDramix® steelfibers, where added to concrete, will enable the latter to sustain higher loads (when compared to plain concrete) after first cracking. In this respect, "Dramix® Pro" is meant to be a methodology that is to allow the users of the Dramix® steelfibers (where such fibers are added to concrete) to determine the performance of Dramix® steelfiber reinforced concrete; performance, as stated above, means the limit between serviceability on the one hand and un-safety on the other hand of Dramix® steelfiber reinforced concrete being submitted to given loads.

Whereas BEKAERT is confident with the scientific quality of "Dramix® Pro" and whereas, as a result thereof, BEKAERT warrants the validity of the software and the resulting design note as a methodology, BEKAERT is nevertheless unable to have an insight in (and a control over) the correctness of the data (such as but not limited to correct loads and material factors) that are actually being used by others for the purpose of any calculation that is being made on the basis of the software.

In addition, BEKAERT is also unable to have an insight in (and a control over) the respect by others of the conditions (such as but not limited to the subbase tolerance, the mixing of Dramix® steelfibers with concrete according to BEKAERT specifications, the timely curing of the concrete, the use of adequate curing components) that are precedent to Dramix® steelfiber reinforced concrete performing as intended.

In respect of what precedes, BEKAERT hereby declines any liability whatsoever for losses and/or damages of whatever kind (and sustained by whomever) that might result either from use by others of erroneous data (where used for the purpose of any calculation that is being made on the basis of the software) or from disrespect by others of any of the conditions that are precedent to Dramix®

steelfiber reinforced concrete performing as intended. BEKAERT can not be considered to be nor to become an architect and/or building engineer on the sole basis of BEKAERT providing to others the Dramix® "design note" and in the same respect, BEKAERT can not be considered to accept any of the liabilities that may possibly devolve on architects and/or building engineers.

Finally, the Dramix® "design note" does not relieve others to test the material properties, equivalent flexural stress, of the Dramix® steelfiber reinforced concrete according to the standards stated above.

By the single fact of utilising the Dramix® "design note", the user accepts and agrees that this utilisation is considered to be done or to have been done under the terms and conditions stated above. By the same fact, the user agrees to waive all rights of subrogation against BEKAERT and/or to hold BEKAERT harmless from and against all claims for all losses and/or damages (of whatever kind and by whomever sustained) for which BEKAERT, pursuant to what precedes, declines liability.

The Dramix® "detailed design note" may not be used for any other purpose than for making



calculations in respect of the Dramix® steelfibers; violation hereof shall entail legal proceedings by BEKAERT in view of indemnification of all losses that BEKAERT may sustain as a result of such violation. At all times, the rights of intellectual property over the Dramix® "detailed design note" will remain vested in BEKAERT; the single fact of the utilisation by others of the Dramix® "detailed design note" can under no circumstances be considered to constitute a transfer to others of the rights of intellectual property over the Dramix® "detailed design note". The sales of the Dramix® "detailed design note" (and/or the commercialising thereof in any other way) to others is strictly prohibited; violation hereof shall entail legal proceedings by BEKAERT in view of indemnification of all losses that BEKAERT may sustain as a result of such violation.



2. Input Data

Load Cases

TWO WHEELLOADS

N° Load Contact Distance

W1 35 kN 0.85 N/mm2 a 1800 mm

W2

EIGHT WHEELLOADS IN A RECTANGLE

N° Load contact

W1,W2 W3,W4 23 kN/ 0.85 N/mm2/ 400 mm

W5,W6 W7,W8 / / 1400 mm

1200 mm



Concrete Characteristics

Following concrete characteristics have been applied in this design.

CONCRETE CHARACTERISTICS

Compressive strength 3000 psi

Flexural strength f fctk 3.40 N/mm2

f fctm 3.40 N/mm2

E-modulus Ec 21350.00 N/mm2

Poisson Coefficient c 0.15

Relaxation factor c 2.60

Shrinkage factor (‰) 'c 0.40

Concrete age correction factor 1 - 28 d.

Resilient Sub-base

• Input

CBR =40.00 %According the Middlebrooks en Bertran graph the equivalent K value isks = 0.109 N/mm3

Elastic radius of rigidity

= 487 mm

= 6142.9 kNm/m

i = 281250.0 mm3/m

= 0.25

Safety Factors

Material Factors Ultimate Limit State

Serviceability Limit State

Concrete 1.50 1.00



SF-concrete 1.20 1.00

Steel 1.15 1.00

Load FactorsVariable Loads 1.20 1.00

Dynamic Factor 1.40 1.00

Dynamic factor

= 1.16 Not used in calculation

N = 100000.00 (Number of load repititions)

Load Transfer

• GeneralA large concrete slab is traditionally divided into smaller areas by means of contraction joints. Aggregate interlock enables to transfer part of the load to the adjacent slab(s). The values taken in this design are based the PCA document for unreinforced concrete. Further research will enable us to enhance these factors.

•Contraction joints

= 1.76 mm

(Xs, Ys, see shrinkage)

= 0.73

•Intersection of two sawcut joints= 0.61

•Doweled joints= 0.60



Perimeter Mesh

• Input

If a mesh for the edge has been selected, it is authomatically assumed that in the corner the same mesh is placed. In the tabels below the values for (m+m') have already been adjusted with the M' the mesh can take.

At = 188 mm2/m Ct = 50 mm

=7.21 kNm M'SLS=8.29 kNm

Ab = 0 mm2/m Cb = 0 mm

=0.00 kNm MSLS= 0.00 kNm



Type of load : WheelloadNumber of loads : 2Positioning of the loads : In line

Location on the floor : Aside the intersection of two contraction joints



Type of load : WheelloadNumber of loads : 8Positioning of the loads : in a rectangle

Location on the floor : Aside the intersection of two contraction joints



Type of load : WheelloadNumber of loads : 2Positioning of the loads : In line

Location on the floor : Over the intersection of two contraction joints



Type of load : WheelloadNumber of loads : 8Positioning of the loads : In a rectangle

Location on the floor : Over the intersection of two contraction joints



Type of load : WheelloadNumber of loads : 2Positioning of the loads : in LineLocation on the floor : Center



Type of load : WheelloadNumber of loads : 8Positioning of the loads : in a rectangleLocation on the floor : Center



Type of load : WheelloadNumber of loads : 2Positioning of the loads : In lineLocation on the floor : Contraction joint



Type of load : WheelloadNumber of loads : 8Positioning of the loads : In a rectangleLocation on the floor : Contraction joint



Type of load : WheelloadNumber of loads : 2Positioning of the loads : In lineLocation on the floor : Doweled expansion joint



Type of load : WheelloadNumber of loads : 8Positioning of the loads : In a rectangleLocation on the floor : Doweled Joint



Type of load : WheelloadNumber of loads : 2Positioning of the loads : In lineLocation on the floor : Edge with a perimeter mesh - Perpendicular



Type of load : WheelloadNumber of loads : 8Positioning of the loads : in a rectangleLocation on the floor : At the edge - Perpendicular



Type of load : WheelloadNumber of loads : 2Positioning of the loads : In lineLocation on the floor : Edge with a perimeter mesh - Parallel



Type of load : WheelloadNumber of loads : 8Positioning of the loads : in a rectangleLocation on the floor : At the edge - Parallel



Shrinkage

• Input

XS = 4400 mm

YS = 4400 mm

XD = 26400 mm

YD = 26400 mm

Temperature

• Input

Tt = 35 C°

Tb = 20 C°

Result

• Structure

A general overview of the design equations is illustrated through the simple example of a concentrated load (Fig. 1). When a concentrated load, much less than the ultimate load, is applied over a small circular area on a relatively large concrete slab, the stresses can be computed for an elastic and infinite plate on an elastic sub-base (See curve one in Fig. 1). The first portion of the curve (up to FR) illustrates this in Figure 2. As the load increases beyond FR, plastic hinges form at the bottom of the slab. Stresses begin to be distributed from the bottom towards the top of the slab at this point. As the load reaches FR’, circumferential hinges form at the top of the slab. Complete failure of the slab occurs by punching shear at a load even greater than FR’, provided the contact area is adequate. Ultimate flexural strength at the bottom and top of the slab cross-section are given by mean equivalent strength (Eqn. 1) and mean modulus of rupture (Eqn. 2) values:



WE DISTINGUISH 2 SITUATIONS

-> There is STRUCTURAL STABILITY when :

-> STRUCTURAL SAFETY is achieved with the following :

Enhance the loads with load factors. (See above) Decrease the admissible stresses with material factors. (See above)

From the yield line analysis and the chosen load cases the following maximum moments were achieved:

Bottom yieldsOccurring moment : mOccurring flexural stress :

Eqn. 1 Top yieldsOccurring moment : m’Occurring flexural stress :

Eqn. 2



Ultimate Limit State Serviceability Limit State

Bending moments (kNm)

Loads (m+m’)max 12.32 kNm (m+m’)max 7.33 kNm

Shrinkage 1.84 kNm

Temperature>

1.95 kNm

Settlement 0.00 kNm

Floor thickness 150 mm

Required SF concrete flexural stress

1.22 N/mm2 0.00 N/mm2

• Materials

Ultimate Limit State Serviceability Limit StateConcrete design stress

2.27 N/mm2 3.40 N/mm2

Dramix type RC 65/60 BN type RC 65/60 BN

Dosage 20 kg/m3 Dosage 20 kg/m3

1.60 N/mm2 1.87 N/mm2

SF Ductility (%)

47.00 55.00

Ultimate Limit State: for a dosage of 20 kg/m3 Dramix RC 65/60 BN.

Serviceability Limit State: for a dosage of 20 kg/m3 Dramix RC 65/60 BN.

DRAMIX® PROPOSAL

• StructureCLIENT STEELSER SAC PROJECT Losa Industrial Piura

OBJECT Losa 1056m2 Con Juntas DESIGN MADE BY Giomar Moya

Please find enclosed a Dramix® Steel Fiber design for concrete slab on grade reinforcement. The Dramix® solution is based on the following assumptions :

Assumptions / Design CriteriaCBR k value : 40.00

Concrete compressive strength, f ck : 3000 psi

For ultimate limit state, the governing load case is :Eight wheels in a rectagle - Saw Cut 12.32 kNm



For serviceability limit state, the governing load case is :Eight wheels in a rectagle - Saw Cut 11.12 kNm

Temperature differential between top and Bottom of the slab 15 °C

Coefficient of friction (µ) between slab and subbase : 1.20

Dramix ® SolutionFloor thickness : 150 mm

Dosage : 20 kg/m3

Fiber type : RC 65/60 BN

Re,3 value : 47.00 %

Equivalent flexural strength (Ffct,eq,150) : 1.60 N/mm2

Max joint spacing : 4400 mm * 4400 mm

NOTE : This proposal is made with the understanding that the slab will be constructed in using the construction recommendations contained in the introduction of this document.

Remarks



MC STEELSER (Almacén Industrial Piura 1056 Con Juntas - Dramix 3D6550 BL 1520)

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