Applied Analysis & Technology © 2015

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Slide 1 of 11

Analysis of Reinforced Concrete (RC) McNeice Slab Using Nonlinear Finite

Element Techniques MSC/Marc

Prepared By:

David R. Dearth, P.E.

Applied Analysis & Technology, Inc.16731 Sea Witch Lane

Huntington Beach, CA 92649

Telephone (714) 846-4235

E-Mail AppliedAT@aol.com

Web Site www.AppliedAnalysisAndTech.com

Applied Analysis & Technology © 2015 Slide 2 of 11

Introduction McNeice (1.) tested a reinforced concrete (RC) slab in 1967.

The purpose of this summary is to present results of addressing this RC Slab and

computing the load deflection curve using MSC/Marc for comparison to the

experimental test data.

For comparison purposes the results from Abaqus example problem 1.1.5 using

Abaqus/Explicate at tension stiffening case ε = 0.002 in/in are also compared.

For rectangular plates (or slabs) no general expression for deflection of plates with

corner supports as a function of central concentrated loading is available. The loading to

produce (a.) initial cracking and (b.) ultimate capacity is computed using the Marc

Vector plots of element cracking strain.

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Applied Analysis & Technology © 2015 Slide 3 of 11

McNeice Slab Geometry with Rebar Definitionfrom Reference 1 No Scale

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Figure 1.1.5-1 McNeice Slab steel reinforcement locations (not to scale)

(Abaqus Examples Manual 1.1.5 Collapse of Concrete Slab)

3” o.c.

Applied Analysis & Technology © 2015

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Quarter Symmetric RC Slab with Boundary Conditions & Loading

X-Z Symmetric

Plane, BC = Ty

Symmetric Loading,

Ptot/4 for Qtr Sym

Idealization

Corner Vertical

Reaction, BC=Tz

Y-Z Symmetric

Plane, BC = Tx

Mesh size for the quarter

symmetric model is 12x12x4

Applied Analysis & Technology © 2015

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Quarter Symmetric RC Slab Rebar Idealization

3/16” dia.

Interior Rebar

Area = 0.0276 in2

3/16” dia. Rebar at

Plane of Symmetry

Area/2 = 0.0138 in2

3/16” dia. Rebar at

Plane of Symmetry

Area/2 = 0.0138 in2

Rebar Material Properties; Mild SteelEs= 29x 106 psi ν =0.3

Yield Stress Fty = 60,000 psi

Bi-Linear-Plastic Modulus = Perfectly Plastic

X-Z Symmetric

Plane, BC = Ty

Y-Z Symmetric

Plane, BC = Tx

Rebar Spacing

3” o.c. Typ

Rebar Size 3/16” Dia.

Table 4.1 Slab No. 1 (1.)

Applied Analysis & Technology © 2015

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Concrete : Isotropic Tension PropertiesThe concrete is idealized using 3D solid elements. Young’s modulus of elasticity for the concrete is given as:

Concrete Material PropertiesEs= 4.150 x 106 psi ν =0.15

Critical Cracking Stress (Rupture Stress) fr = 460 psi(2.)

Tension Softening Strain at Failure, ε = 0.002 in/in(2.)

Note: Abaqus input is “strain at failure”.

Marc input is “tension softening slope”.

Applied Analysis & Technology © 2015

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Slide 7 of 11

Concrete : Isotropic Compression Properties

The concrete is idealized using 3D solid elements. Young’s modulus of elasticity for the concrete is given as:

Concrete Material PropertiesEs= 4.150 x 106 psi ν =0.15

Compressive Failure Stress f’c = 5,550 psi(2.)

Crushing Strain, εc = 0.003 in/in (assumed)

Note: Plasticity definition data for MSC/Marc is defined as post-yield, or plastic, portion of the stress strain curve; e.g. yield

stress zero net plasticity. Typical engineering data for stress-strain curves are defined as total nominal strain.

The compressive uniaxial stress-

strain relationship for the concrete

model was obtained using the multi-

linear isotropic stress-strain

equations for concrete from

MacGregor 1992(3.).

Applied Analysis & Technology © 2015

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Concrete : Isotropic Properties

The concrete is idealized using 3D solid elements. Young’s modulus of elasticity for the concrete is given as:

Concrete Material PropertiesElastic : Ee= 4.15 x106 psi ν = 0.15

Cracking : Critical Cracking Stress (Rupture Stress) fr = 460 psi

Softening Modulus, Es= 243,495 psi [Failure Strain = 0.002 in/in]

Crushing Strain, εc = 0.003 in/in, Shear Retention : 20%

Plasticity : Elastic-Plastic, Isotropic Hardening, Buyukozturk Concrete

Concrete Isotropic Material Input Dialog

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Rev “x”McNeice Slab Test Deflections vs MSC/Marc & Abaqus/Explicit

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Rev “x”Marc Concrete Crack Progression for McNeice Slab

660 lbs. Last Load Step Prior to Cracks

Crack Progression vs. Slab Loading

832 lbs. Cracks Begin to Appear

At Slab Center and Corner Support

1,286 lbs. Crack Propagation

At Slab Center and Corner Support

1,532 lbs. Crack Propagation

At Slab Center Out to Edges and

Corner Support

1,940 lbs. Crack Propagation

At Slab Center Out to Edges and

Corner Support

3,498 lbs. Crack Propagation

At Ultimate Load Prior to Full

Collapse

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References1) McNeice, G.M., Elastic-Plastic Bending of Plates and Slabs by Finite Element

Method; Thesis Submitted to University of London for Degree Doctor of Philosophy,

Department of Civil and Municipal Engineering University College of London,

November 1967

2) Dassault Systems, 1.1.5 Collapse of Concrete Slab, Abaqus 6.11 Example Problems

Manual, Volume 1: Static and Dynamic Analyses, 2011

3) MacGregor, J.G. (1992), Reinforced Concrete Mechanics and Design, Prentice-Hall,

Inc., Englewood Cliffs, NJ.

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