Christos C. Chamis

Glenn Research Center, Cleveland, Ohio

Pascal K. Gotsis

Technical Education Institute, Serres, Greece

Application of Composite Mechanics

to Composites Enhanced Concrete Structures

NASA/TM—2006-214038

January 2006
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Christos C. Chamis

Glenn Research Center, Cleveland, Ohio

Pascal K. Gotsis

Technical Education Institute, Serres, Greece

Application of Composite Mechanics

to Composites Enhanced Concrete Structures

NASA/TM—2006-214038

January 2006

National Aeronautics and

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Glenn Research Center

Prepared for the

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NASA/TM—2006-214038 1

Application of Composite Mechanics to Composites 

Enhanced Concrete Structures 

Christos C. Chamis 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Pascal K. Gotsis 

Technical Education Institute 

Terma Magnisias Str 

TK62124, Serres, Greece 

Abstract 

A new and effective method is described to design composites to repair damage or enhance the 

overload strength of concrete infrastructures. The method is based on composite mechanics which is 

available in computer codes. It is used to simulate structural sections made from reinforced concrete 

which are typical in infrastructure as well as select reinforced concrete structures. The structural sections 

are represented by a number of layers through the thickness where different layers are used in concrete, 

and for the composite. The reinforced concrete structures are represented with finite elements where the 

element stiffness parameters are from the structural sections which are represented by composite 

mechanics. The load carrying capability of the structure is determined by progressive structural fractural. 

Results show up to 40 percent improvements for damage and for overload enhancement with relatively 

small laminate thickness for the structural sections and up to three times for the composite enhanced 

select structures (arches and domes). 

Introduction 

Reinforced concrete is widely used in the construction industry. Concrete tends to crack, chip and be 

damaged as a result of inadvertent loads or overloads which may not have been accounted for in the initial 

design. The damage in concrete structures may extend to a state where the safety of that structure 

becomes a major concern. Recently, a considerable effort is being expended on repairing damaged or 

upgrading concrete structures by using fiber reinforced composites. For example, several sessions were 

devoted to this subject at a recent International SAMPE Symposium and Exhibition, Long Beach, 

California (ref. 1). The use of composites is natural since the repairing composites tend to be thin 

laminates which are easily bonded to damaged concrete structures made from cylindrical and flat surfaces 

in general. Different methods for designing and analyzing thin laminates have been developed and are 

available in many computer codes. Recent research demonstrates that damaged concrete structures and 

their repairing composites can be simulated simultaneously by composite mechanics which is available in 

some of those computer codes (refs. 2 to 3). By using composite mechanics, we can represent any 

concrete structural section by assuming that it consists of several layers through its thickness. In so doing, 

we take advantage of all the features available in computer codes for composite mechanics—for example, 

ICAN (Integrated Composite Analyzer) (ref. 4). The objective of the proposed paper is to describe those 

features and attendant computer codes, and illustrate their application to select reinforced concrete 

structural sections and structures. The composite mechanics is described briefly. Then, it is applied to 

select structural sections and to select structures (special arch and a dome). Note that results presented 

herein are computational. Comparisons with other methods and concrete code requirements are included 

in the references cited. 
NASA/TM—2006-214038 2

Composite Mechanics 

Composite behavior is simulated by assuming that the composite consists of several layers (plies) 

through its thickness. The plies include both fiber and matrix. Theoretically, we can represent any 

concrete structural section by assuming that it consists only of several layers through its thickness where: 

(1) most layers consist only of concrete (matrix); (2) one or two layers consists of concrete and steel Rbars (matrix and fibers); (3) one or several layers of the composite repair laminate. Composite mechanics 

is natural, then, since we can represent concrete structural sections as layers and also composite laminates 

as layers. By so doing, we take advantage of all the features available in computer codes for composite 

mechanics—for example, ICAN (ref. 4). 

Brief Description of ICAN Features 

A brief description of ICAN features is instructive because it demonstrates its versatility and ideal 

application to reinforced concrete. ICAN evolved from research conducted in composite micromechanics 

and macromechanics over the last four decades at NASA Glenn Research Center. The primary goal of 

that research is to develop composite mechanics theories and structural analysis methods that range in 

scale from micromechanics to structural analysis in one integrated code, figure 1, (ref. 4). The 

micromechanics theories are represented by simplified equations that have been corroborated by detailed 

three-dimensional finite element analyses (ref. 5). ICAN is designed to carry out a comprehensive 

analysis including the hygral, thermal and mechanical properties/responses of multilayered continuous 

fiber reinforced polymer matrix composites. The analysis contains the essential features required to obtain 

the material properties integrated through the thickness to effectively design structural components made 

from fiber composites. It can analyze standard composites, i.e., composites consisting of one type of fiber 

in a matrix forming a ply lamina or a layer. In addition to that, the code can also analyze an interplay or 

intraply hybrid composite system. This is a useful feature because different types of R-bars can be 

included in the same section. These layers are then arranged with prescribed orientations to form a 

composite laminate. The micromechanics equations in ICAN take into account the effects of temperature 

and/or moisture gradients through the thickness. This feature can be very useful in modeling curing of 

concrete or degradation in moist-type environments. However, within each layer, the temperature or 

moisture is assumed to be constant. ICAN includes a dedicated databank of constituent material 

properties of commonly available fibers and matrices, and also allows the user to build in a very userfriendly manner, a database of new material properties when they become available. The user needs to 

specify only a code name of constituent and the code gets all the appropriate material properties from the 

databank. 

Input to ICAN includes composite geometry, i.e., the ply or the layer lay-up and fiber volume ratios, 

thicknesses and the orientations of the layers, code names for the constituent materials, factors reflecting 

the fabrication process and the loading conditions. ICAN performs a micromechanics and 

macromechanics analysis of the laminate, ICAN output includes the various ply and composite properties, 

composite structural response, and composite stress analysis results with details of failure. Additional 

features unique to ICAN include ply stress-strain relations, stress concentrations around a circular hole, 

free-edge stresses, material properties input for finite element analysis using MSC/NASTRAN and other 

general purpose finite element codes, failure loads based on maximum stress criterion and laminate 

failure stresses based on first-ply failures, etc. The output from the program can be tailored to specific 

needs of the user by choosing the appropriate options in the input file. Integration of ICAN with general 

purpose finite elements structural analysis is shown schematically in figure 1 and will be discussed further 

in a later section when structural progressive fracture is simulated. Detailed application of ICAN to 

concrete is described (ref. 3). 
NASA/TM—2006-214038 3

Composite Enhanced Reinforced Concrete Structural Sections 

The concept is first demonstrated by applying it to a one and two way reinforced concrete section. 

Then it is applied to a special arch and a dome both made from reinforced concrete. 

The section investigated is h = 25.4 cm (10 in.) deep by b = 15.24 cm (6 in.) wide. It is one-way 

reinforced with 1.27 cm (0.50 in.) diameter steel reinforced bars (fig. 2(a)). The section is represented by 

plies as shown in figure 2(a). For this application, it was assumed that the section was damaged (cracked 

at the bottom) and was subsequently repaired by unidirectional composite laminates. The properties 

assumed for the different materials were: concrete modulus = 20.68 GPa (3 Mpsi), strength = 2.07 MPA 

(300 psi) tension, 20.7 MPa (3,000 psi) compressions; steel modulus = 206.8 GPa (30 Mpsi), yield 

strength 137.9 MPa (20,000 psi) tension. The area of the reinforcing steel bars is 4.5 percent of the 

concrete structural section (h × b, fig. 2(a)). The section is enhanced with E-Glass/Epoxy with a 0.55 fiber 

volume ratio, composite modulus = 38.0 GPa (5.5 Mpsi) and tensile strength = 1.38 MPa (200 ksi). The 

results obtained for the one-way section are plotted in figure 3. As can be seen, the enhancement is 

substantial (two times) for a relatively small composite thickness and increases linearly with composite 

thickness. Comparable results for the two-way slab (fig. 2(b)) are plotted in figure 4. The enhancements 

are even greater than for the one-way slab. 
NASA/TM—2006-214038 4
NASA/TM—2006-214038 5

Composite Enhanced Special Reinforced Concrete Arch 

The special arch has a 20 m (65 ft 8 in.) chord length and a 6 m (20 ft) height (rise); the thickness of 

the arch 25.4 cm (10 in.). The structural section is reinforced with two-way steel at the inner, outer, and 

mid surfaces. The total volume ratio of the steel in the section is 0.67 percent. The arch is 26.0 cm 

(10 ft 3 in.) wide at the base and 32 cm (1 ft 7 in.) wide at the crown. A finite element model schematic of 

the arch and its structural sections are shown in figure 5. The arch is first evaluated without composite 

enhancement for two different load conditions; concentrated load at the crown and uniform pressure. 

Subsequently, it is re-evaluated with composite enhancements. The load carrying capacity of the 

reinforced concrete arch (without the composite enhancement) is determined incrementally by 

progressive fracture by using CODSTRAN (ref. 6). The concentrated fracture load obtained by using 

CODSTRAN is 172.4 KN (38.8 Kips) while the collapse pressure is 0.019 MPa (2.8) psi. The 

CODSTRAN results for progressive fracture are show (fig. 6) for the concentrated load and in figure 7 for 

the uniform pressure. Two curves are plotted in each figure, one is for the accumulation of progressive 

damage and the other is for the vertical displacement at the crown. Note both of the curves are normalized 

by their respective maximum values as noted in those figures. The important observations from the curves 

in figure 6 are: 1) the crown displacement curve is smooth while 2) the cumulative progressive fracture is 

very non-smooth. The deviations from non-smooth indicate discontinuities (jumps) in the damaged 

volume where load magnitudes for damage initiation, slow growth, and rapid propagation to fracture are 

easily identifiable. Examining the curves in figure 7, it is seen that the vertical displacement is smooth 

and nonlinear, and the progressive damage accumulation is smoother than that for the concentrated load. 

However, pressure at which damage initiation, slow and rapid progression to fracture occur, are readily 

identifiable. 
NASA/TM—2006-214038 6
NASA/TM—2006-214038 7

The degradation of structural performance of the arch with respect to other structural performance 

variables such as frequencies and buckling loads can be readily evaluated at the end of each load 

increment when the damaged structure is in equilibrium with the applied external loads. For example, the 

degradation of the concentrated buckling load of the arch is shown in figure 8, and for its first four 

vibration frequencies is shown in figure 9. As can be seen in figure, the buckling load starts to degrade 

with damage initiation (fig. 6) is at about 10 percent of the fracture load and continues to degrade rapidly 

with damage accumulation. The degradation of the vibration frequencies (fig. 9) is not as rapid as that for 

the buckling load. The important conclusion from the evaluation of the special arch is that composite 

mechanics coupled with finite element structural analysis provide unique capability to evaluate the 

structural performance of reinforced concrete structures. The arch was enhanced by applying composite 

layers. The composite layers consist of E-glass/epoxy at about 0.55 fiber volume ratio. The layer 

thickness was 1.27 cm (0.50 in.). The results for progressive damage and structural fracture are shown in 

figure 10. Three curves are plotted in this figure. One is the same as that for the un-enhanced arch (fig. 6). 

The other two are for the composite enhanced load carrying capability of the arch—one on the top surface 

and one on the bottom surface. As can be seen, the enhancements are substantial when the composite is 

placed on the bottom surface. 
NASA/TM—2006-214038 8
NASA/TM—2006-214038 9

Composite Enhanced Reinforced Concrete Dome

The concrete dome has 20 m (65 ft 8 in.) chord and 6 m (20 ft) high rise. The structural section is 

identical to that for the special arch (fig. 5(b)). A finite element model schematic of the dome is shown in 

figure 11. The dome is first evaluated without the composite enhancement and then with it. The fracture 

dome is subjected to two different loading conditions; concentrated load at the crown and uniform 

pressure load. The fracture load for both conditions is determined by cumulative progressive structural 

fracture by using CODSTRAN (ref. 6). The concentrated fracture load for the dome obtained by using 

CODSTRAN is 310 KN (69.72 Kips) while that for the uniform pressure is 0.34 MPa (4.91) psi. 

Normalized values of the crown vertical displacement and the damage accumulated are plotted versus 

normalized force in figure 12 for the concentrated load and in figure 13 for the uniform pressure. 

Examining the two curves in figure 12, it is seen that the vertical displacement is almost linear to about 

30 percent from the structural fracture loads damage initiates at about 4 percent of the fracture loads. Both 

damage progression and vertical displacement increase very rapidly as the fracture load is approached. 

Note that there is less slow damage growth compared to that of the arch. One conclusion from figure 12 is 

that the dome exhibits limited damage tolerance when subjected to concentrated load at the crown. 

Normalized values of the crown vertical displacement and the accumulated damage are plotted versus 

normalized pressure in figure 13. The important observation from these curves is that the dome exhibits 

linear behavior until very close (within 2 percent) to the fracture pressure. Damage initiates sat about 

98 percent of the fracture pressure and increases very rapidly for the next 2 percent to fracture. There is a 

rapid increase in the crown vertical displacement in the remaining last 2 percent of the load. The 

important conclusion is that the reinforced concrete domes subjected to uniform pressure provide no 

discriminating information of imminent fracture. 
NASA/TM—2006-214038 10
NASA/TM—2006-214038 11

The buckling load of the un-enhanced dome, subjected to concentrated load at the crown, is shown in 

figure 14 where normalized values are plotted. It is seen that the buckling load is very, very high 

compared to the fracture load (at least 100 times). It is also seen that buckling load starts degrading at 

about 23 percent of the fracture load. This latter result is interesting because it indicates that progressive 

damage must initiate at about this value. Re-examination of the curves in figure 12 reveals that this is 

consistent with the point at which damage initiates. Note that the buckling load decreases to about 

50 percent just prior to fracture. The degradation in the first four vibration modes is shown in figure 15. 

Insignificant or negligible degradation occurs prior to fracture. Apparently, the frequencies are not as 

sensitive a measure or degradation as is the buckling load. 

The reinforced concrete dome is enhanced with the same composite layers as is the special arch. The 

enhanced results are shown in figure 16 where the damage is plotted versus load for three different cases: 

un-enhanced, composite enhanced at the top, and composite enhanced at the bottom. It is very interesting 

to note that the composite enhancement at the top increases the fracture load by twofold, while that at the 

bottom only about 20 percent. 

The important conclusions are: 1) the load carrying capacity of reinforced concrete structures can be 

substantially enhanced by the judicious use of fiber composite layers and 2) computational simulation 

capabilities which are suitable combinations of composite mechanics and general finite element structural 

analysis appear to be appropriate to evaluate composite enhanced reinforced concrete structures. 
NASA/TM—2006-214038 12
NASA/TM—2006-214038 13

General Comments

The results presented previously constitute a relatively small sample of what can be done by using 

composite mechanics in conjunction with general purpose finite element structural analysis and composite 

structural progressive fracture concepts. Obviously, any structural component or assemblies of structural 

components can be simulated for load carrying capability; fracture loads setting safety factors; designing 

monitoring devices; scheduling inspection intervals; planning repairs; a composite enhancement that is 

relatively thin compared to the section and does not introduce asymmetries. Even if it did, composite 

mechanics and the finite element structural analysis will account for any asymmetry effects on the section 

performance. 

Conclusions 

The important conclusions from an investigation to use composite mechanics for designing composite 

enhanced structural sections and structures are: 

• Composite mechanics can be used to design un-enhanced and enhanced reinforced concrete 

structural sections. 

• Substantial increases in load carrying capacities can be obtained (at least two times) with relatively 

thin composite layer enhancements. 

• Composite mechanics in conjunction with general purpose finite element structural analysis and 

composite structural progressive fracture can be used to obtain the load carry carrying enhancement 

of reinforced concrete structures. These load enhancements can be as high as three times that of the 

un-enhanced. 
NASA/TM—2006-214038 14

• Structural degradation resulting from progressive fracture can be evaluated for losses in buckling 

loads and vibration frequencies. Buckling loads are more sensitive to damage than vibration 

frequencies. 

• The damage tolerance of reinforced concrete structures and those with composite enhancements can 

be evaluated from the progressive structural fracture history as the magnitude of damage sustained 

from damage initiation to damage for imminent structural fracture. 

• The combination of composite mechanics with finite element structural analysis and composite 

progressive fracture is sufficiently general and can be applied to all type of non-enhanced and 

composite enhanced reinforced concrete structures. 

References

1. Several volumes of Spring Conferences, SAMPE, Covina, CA. 

2. Mital, S.K., Gotsis, P.K. and Chamis, C.C., “Laminate Analogy for Composites Application to 

Infrastructures.” Invited paper for the Conference Proceedings of International SAMPE Symposium 

42, May 3–5, 1997, Anaheim, CA. 

3. Mital, S.K. and Chamis, C.C., “Thermal and Mechanical Behavior of Particulate Composite 

Materials, Materials and Design Technology, ASME. PD. 62.275, (1994). 

4. Murthy, P.L.N., Ginty, C.A. and Santfeliz, J.G., “Second Generation Integrated Composite Analyzer 

(ICAN) Computer Code.” NASA TP–3200, (1993). 

5. Caruso, J.J. and Chamis, C.C., Journal of Composite Technology & Research, Vol. 8(3) 77, (1986). 

6. Chamix, C.C., Murthy, P.L.N. and Minnetyan, L., “Progressive Fracture of Polymer Matrix 

Composite Structures.” Elsevier Science B.V., reprinted from Theoretical and Applied Fracture 

Mechanics. 25, 1 (1996). 
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E–15395

WBS 561581.02.08.03

20

Application of Composite Mechanics to Composites Enhanced

Concrete Structures

Christos C. Chamis and Pascal K. Gotsis

Displacement; Energy; Finite elements; Stresses

Unclassified -Unlimited

Subject Category: 39

Prepared for the 16th European Conference of Fracture cosponsored by ESIS, ASTM, SMS, AIAS, JSEM, BSSM, SEM,

and EURASEM, Alexandroupolis, Greece, July 3–7, 2006. Christos C. Chamis, e-mail: Christos.C.Chamis@nasa.gov,

NASA Glenn Research Center; and Pascal K. Gotsis, e-mail: pkgotsis@email.teiser.gr, Technical Education Institute,

Terma Magnisias Str, TK62124, Serres, Greece. Responsible person, Christos C. Chamis, organization code

R, 216–433–3252.

A new and effective method is described to design composites to repair damage or enhance the overload strength of

concrete infrastructures. The method is based on composite mechanics which is available in computer codes. It is used

 to simulate structural sections made from reinforced concrete which are typical in infrastructure as well as select

reinforced concrete structures. The structural sections are represented by a number of layers through the thickness

where different layers are used in concrete, and for the composite. The reinforced concrete structures are represented

with finite elements where the element stiffness parameters are from the structural sections which are represented by

composite mechanics. The load carrying capability of the structure is determined by progressive structural fractural.

Results show up to 40 percent improvements for damage and for overload enhancement with relatively small

laminate thickness for the structural sections and up to three times for the composite enhanced select structures

(arches and domes).