Analysis McNeice Slab MSC-Marc

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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 [email protected]

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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McNeice Slab Geometry with Rebar Definition

from 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)

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Quarter Symmetric RC Slab with Boundary Conditions & Loading

X-Z Symmetric Plane, BC = Ty

Symmetric Loading, P_tot/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

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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 Steel

E_s= 29x 106_{psi ν =0.3}

Yield Stress F_ty= 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.)

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Concrete : Isotropic Tension Properties

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

Concrete Material Properties

E_s= 4.150 x 106_{psi ν =0.15}

Critical Cracking Stress (Rupture Stress) f_r= 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”.

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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 Properties

E_s= 4.150 x 106_{psi ν =0.15}

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

Crushing Strain, ε_c= 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.)_.

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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 Properties

Elastic : E_e= 4.15 x106_{psi ν = 0.15}

Cracking : Critical Cracking Stress (Rupture Stress) f_r= 460 psi Softening Modulus, E_s= 243,495 psi [Failure Strain = 0.002 in/in] Crushing Strain, ε_c= 0.003 in/in, Shear Retention : 20%

Plasticity : Elastic-Plastic, Isotropic Hardening, Buyukozturk Concrete Concrete Isotropic Material Input Dialog

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Marc Concrete Crack Progression for McNeice Slab

660 lbs. Last Load Step Prior to Cracks

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

References

1) 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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