Enhancing ferrocement performance: plastic analysis for bending strength prediction

ABSTRACT

In this paper, a study has been made to understand the strength and behavior of fabricated Ferro cement elements under four-point bending. The size of the element adopted in this study is 800 mm × 150 mm × 50 mm. A mortar mix 1:1.1 by weight with w/c ratio 0.36 was adopted. Variables of the study include the number of layers of wire mesh. The number of mesh layers varied is 0, 3, 4, 5 and 6. From the test results it was observed that both first crack and ultimate moments were increased with the increase in volume fraction of reinforcement. It was also observed that the crack width is efficiently controlled by the higher volume fraction of mesh reinforcement. The ultimate moment capacity of the Ferro cement elements are calculated by two methods. The first method is based on the concept of conventional reinforced concrete theory and second method is based on the concept of plastic analysis. A comparison of the ultimate moments predicted from elastic and plastic analysis theories with experimental data shows good agreement.

Keywords:
Ferrocement; Flexural strength; Plastic analysis; Crack width control; Reinforcement ratio

1. INTRODUCTION

Ferro cement is a thin composite made with cement-based mortar matrix reinforced with closely spaced layers of small diameter wire mesh. It possesses several technical advantages, such as light weight, high tensile strength to weight ratio, better resistance to crack propagation, easy fabrication to any shape and size and cost of form work and economy. Hence, its applications are wider, which include agriculture, water supply, sanitation, housing and irrigation. Recently, flexural strength prediction has increasingly leveraged finite element (FE) modelling to capture cracking, stiffness degradation, and failure progression with higher fidelity than closed-form sectional approaches. Nonlinear FE frameworks implemented in platforms such as ABAQUS have been used to simulate the flexural response of concrete beams strengthened with externally bonded FRP systems, including explicit calibration of interfacial behaviour and fracture evolution. Extended finite element methods (XFEM) coupled with traction–separation or cohesive constitutive laws have also been adopted to represent discontinuous cracking and debonding mechanisms, enabling validated prediction of ultimate flexural capacity and crack patterns under bending. Representative recent studies include FE-based prediction of flexural strength for FRP-strengthened beam configurations and XFEM-based modelling strategies that reproduce experimental load–deflection response and failure modes with good agreement. Accordingly, the present study adopts a plastic analysis idealization to provide a direct and transparent estimate of ultimate moment capacity for thin ferrocement plate elements with multiple mesh layers, and the predictions are assessed against experimental four-point bending results.

Extensive investigations had been carried out during the last three decades on ferrocement in analytical and experimental works. In case of flexure, ultimate strength models had been proposed by LOGAN and SHAH [¹], JOHNSTON and MOWAT [²], RAJAGOPALAN and PARAMESWARAN [³], BALAGURU et al. [⁴] and HUQ and PAMA [⁵]. These methods are primarily based on the concept of conventional reinforced concrete analysis using the principles of equilibrium and strain compatibility. However, the basic differences are in the assumed compressive stress block, the stress-strain relationship for steel and the failure criterion, i.e. the maximum compressive strain in the matrix. Although simple and rational, these methods require a tedious trial and error approach unsuitable for direct design of ferrocement elements by manual computations. MANSUR and PARAMASIVAM [⁶] proposed a simple method to predict ultimate moment capacity of ferrocement based on plastic analysis approach. CHANDRASEKHAR RAO et al. [⁷] conducted an experimental investigation on solid and voided ferrocement channel beams under flexural loading Test results indicate that the drop in flexural strength with the voids is negligible compared to the decrease in the weight of the member. The moment-curvature response of the voided members under flexural loading improved with the post-ductility of the member with increase in the number of layers. CHANDRASEKHAR RAO et al. [⁸] studied the bending response of thin webbed ferrocement channel sections. Analytical equations are also proposed to predict the ultimate moment capacity of channel units. A comparison of the predicted ultimate moments with test data shows good agreement. Keeping above studies in view, an experimental program has been planned to study the ultimate strength and behavior of ferrocement plate elements in bending. To predict the moment of resistance of the plate elements two methods were adopted based on reinforced concrete theory (elastic) and plastic analysis approach. In plastic analysis approach the ferrocement composite is considered as a homogeneous perfectly elastic–plastic material. AMERICAN CONCRETE INSTITUTE [⁹, ¹⁰] suggests the failure modes of ferrocement under any load is progressive rather than brittle, the load deflection behaviour of any ferrocement element shows post-cracking deformation capacity, energy absorption and toughness. Simple derived equations are adopted for direct design of a cross section. MAULANA et al. [¹¹] developed a finite element–based strength prediction model for notched foamed concrete beams strengthened with KFRP plates under flexural loading. The study demonstrated that FEM can reliably capture crack localization, stress redistribution, and ultimate flexural capacity in strengthened concrete members. OMAR et al. [¹²] developed an extended finite element (XFEM) numerical model to predict flexural strength and crack propagation in concrete beam elements subjected to bending. The model showed good agreement with experimental load–deflection responses and observed failure modes, confirming the effectiveness of advanced FEM approaches for flexural strength prediction. AZMAN [¹³] developed a nonlinear finite element model to predict the flexural behaviour of CFRP-strengthened reinforced concrete beams. The numerical results showed close agreement with experimental flexural capacity and crack distribution, confirming the reliability of FEM for flexural strength prediction. DE BORST et al. [¹⁴] employed an extended finite element method (XFEM) to model crack initiation and propagation in concrete beams subjected to flexural loading. The study demonstrated that XFEM can accurately predict fracture behaviour and ultimate flexural strength without the need for predefined crack paths. SELVARAJAN et al. [¹⁵] investigated the flexural characteristics of ferrocement slabs incorporating geopolymer and to evaluate the most effective composition. When compared to conventional ferrocement slabs, the testing result show that the combination application of GGBS and Nano silica improves flexural strength, stiffness, and crack control. The flexural response was simulated numerically using FEA and the analytical results indicated excellent concordance with experimental results.

2. EXPERIMENTAL PROGRAM

Ordinary portland cement of 53 grade, fine aggregate conforming to the requirements of zone II of IS 383:1970 [¹⁶] were used in the ratio of 1:1.1 with water to binder ratio of 0.36, cement is replaced with 5% silicafume, 5% GGBS and sodium naphthalene formaldehyde (SNF) based super plasticizer of 0.6 percent by weight of the binder are used in the investigation. The specific gravities of cement and fine aggregate are 3.15 and 2.65 respectively. Galvanized iron square woven mesh is used as reinforcement to the ferrocement elements. The diameter of wire is found to be 0.5 mm. The openings in the mesh are 2 mm × 2 mm. The yield strength of the wires of the mesh is found to be 380 MPa. A cement sand ratio of 1:1.1 and a water cement ratio of 0.36 are used for casting the units. The compressive strength of the mortar is found to be 65 MPa, while the split tensile strength of the same is found to be 5.42 MPa.

The test specimens considered for the study were 800 mm × 150 mm × 50 mm. Total twenty plate elements were cast and tested for two different flexure spans. The twenty specimens are divided into two series namely, ‘A’ and ‘B’. The specimens were tested under flexural spans 150 mm and 100 mm for A & B series respectively. Specimens in each series cast with 0, 3, 4, 5 and 6 layers of wire mesh as reinforcement in the ferrocement composite. The plate specimens were cast on vibrating table using plywood moulds. They were demoulded the next day and cured under water at ambient temperature for 28 days. The specimens were then air dried in the laboratory before testing.

All the specimens are tested on universal testing machine of 100-ton capacity. The load was transferred as a two-point symmetrical load as shown in Figure 1a. Deflections were measured under the loading points and at mid-span using deflection gauge of 0.01 mm at least count. During testing, the cracks were developed on the plate and corresponding load for each crack was noted. The first crack was developed at center of bottom surface (tension face) and as the applied load increased, the crack propagated towards the compression face of the plate element.

Figure 1
(a) Test set-up; (b) A-series; (c) B-series; (d) Experimental test setup.

3. TEST RESULTS AND DISCUSSIONS

3.1. General behavior

The load-deflection curves of the specimens have indicated linear behavior up to about the cracking load. As shown in Table 1, the observed first cracking moment increases with increase in the volume fraction of the reinforcement. After cracking (i.e. first cracking load), the load-deflection curve deviated from linearity and gradually become nonlinear (Figure 2). The cracking load is taken as the bend over point in the load-deflection curve of the plate element. Simultaneously several new cracks were formed at finite spacing. The specimens then maintained approximately the same load level with increasing deflection, but the cracks continued to penetrate deep into the top layers of specimens. At this stage, no crushing of the matrix was observed on the compression face. Further increase in deflection was associated with a drop in the applied load. Finally, the specimens collapsed due to fracture of the steel reinforcement. The typical crack patterns of the specimens at ultimate load are shown in Figure 3. It was observed that the number of cracks depends on the volume fraction of reinforcement. Also, from this observation it is understood that a higher volume fraction of reinforcement provides better crack control mechanism by the formation of a large number of well distributed cracks.

Table 1
Test results.

TEST SERIES	SHER SPAN TO DEPTH (a/d) RATIO	NO. OF LAYERS OF WIRE MESH	VOLUME FRACTION OF MESH REINFORCEMENT (NO. OF LAYERS) Vf (%)	EXPERIMENTAL MOMENTS
				FIRST CRACKING MOMENT (Mcr) N-m	ULTIMATE MOMENT (Mtest) N-m
A3L	5.5	3	1.425	110.252	177.813
A4L	5.5	4	1.90	131.50	232.988
A5L	5.5	5	2.375	154.72	269.775
A6L	5.5	6	2.850	177.74	300.438
B3L	6	3	1.425	127.167	206.010
B4L	6	4	1.90	155.88	275.910
B5L	6	5	2.375	184.148	322.26
B6L	6	6	2.850	212.449	359.040

Figure 2
Comparison of load-deflection response of specimens with 6 layers of mesh reinforcement of A & B series.

Figure 3
(a) (b) (c) & (d) Typical crack patterns of ferrocement plates with different (V_f) layers of mesh reinforcement.

3.2. Crack width

All cracks, which appeared at every loading stage, were identified and maximum width of each crack across the width of the specimen was measured by using a portable microscope with an accuracy of ± 0.02 mm to determine the maximum and average crack widths. Figure 3 shows typical crack pattern of the test specimens for different volume fractions of the mesh reinforcement. It is obvious that a higher amount of reinforcement is more effective in crack control mechanism. It was also observed that the maximum crack width decreased with an increase in the volume fraction of reinforcement throughout the entire loading range. Figures 4a and 4b represents the typical load vs. maximum crack width curves for A and B series specimens with different volume fractions of the mesh reinforcement.

Figure 4
(a) Load vs maximum crack width (A-Series); (b) Load vs maximum crack width (B-Series).

3.3. Ultimate strength

The experimental cracking and ultimate moments of the specimens as summarized in Table 1, indicate that the increase in volume fraction of mesh reinforcement will improve the cracking and ultimate moment of the Ferro cement plate elements. However, the V_f has substantial influence on ultimate moment compared to cracking moment, because the main load sharing element in Ferro cement composite is mesh reinforcement only. Experimental moments are now compared with the ultimate moments computed from the methods of conventional reinforced concrete theory based on the principles of equilibrium and strain compatibility (elastic) and plastic analysis theory.

3.3.1. Plastic analysis approach

In elastic theory method a trial-and-error procedure is used to locate the neutral axis and hence to calculate the bending moment capacity of a Ferro cement element. Since several layers of reinforcing meshes are usually involved in Ferro cement, this method is not suitable for hand computations. A simple method based on the concept of plastic analysis is proposed herein to calculate the ultimate moment capacity of the Ferro cement.

Assumptions adopted in this method

1. Plane sections before bending remain plane after bending.

2. Perfect bond exists between the wire meshes and matrix.

3. Skeletal steel, which is primarily required for stability of the element during casting, is ignored.

4. Ferro cement, matrix (mortar) reinforced with uniformly distributed fine wire mesh, is considered as a homogeneous ideally elastic-plastic material having different stress-strain and strength characteristics in tension and compression.

Like reinforced concrete flexure theory, it is reasonable to assume zero tensile strength for the matrix. In compression, the stress-strain relationship depends on variety of factors; however, in the present analysis, the rectangular-parabolic stress-strain relationship as recommended in the reinforced concrete code IS 456-2000 [¹⁷] for concrete may be assumed with a partial safety factor of unity. As shown in Figure 5a the parabolic portion of the curve may be idealized by a straight line giving the bilinear response as indicated by the solid line. The factor of 0.67 allows for the difference between the bending strength and the cube crushing strength f_cu of the concrete. In case of Ferro cement, studies conducted in direct compression [², ⁷] have shown that neither ultimate strength nor the stress-strain characteristics differ significantly from those of the reinforced matrix, if the reinforcing meshes do not provide any confinement to the matrix. Hence the bilinear relationship shown in Figure 5a is equally applicable to Ferro cement.

Figure 5
(a) Idealized stress-strain curve for ferrocement; (b) Idealized stress-strain curve for matrix curve.

The idealised stress–strain curve for ferrocement shown in Figure 5a is based on the composite action between mortar and distributed wire mesh reinforcement, where post-cracking tensile resistance is sustained through crack-bridging and stress redistribution mechanisms. Similarly, the matrix stress–strain idealization in Figure 5b represents a force-equivalent approximation of the nonlinear compressive behaviour of mortar, consistent with experimentally reported parabolic-to-rectangular response models.

Unlike conventional reinforced concrete beams, ferrocement elements derive their flexural resistance from uniformly distributed wire-mesh reinforcement across the thickness, resulting in fundamentally different crack control and fracture behaviour. Following the initiation of matrix cracking, the tensile response of ferrocement is governed predominantly by the effective wire-mesh reinforcement, which continues to carry load through crack-bridging and stress-redistribution mechanisms. The tensile strength of the mortar matrix is therefore limited to controlling crack initiation, while the post-cracking and ultimate tensile load-carrying capacity of the composite are dictated by the distributed reinforcement.

In direct tension, ferrocement behaves as a distributed steel–mortar composite. After matrix cracking, the tensile force is primarily carried by the wire-mesh reinforcement through crack-bridging, while the cracked mortar contributes only secondary tension-stiffening. This behaviour has been consistently adopted in classical ferrocement modelling, where the ultimate tensile capacity is taken as the maximum tensile force that can be transmitted by the effective steel area in the loading direction [², ⁵]. Under this widely used assumption, the internal tensile resultant at ultimate is

(1) $${\mathit{T}}_{\mathit{u}}\approx {\mathit{A}}_{\mathit{s}}\mathrm{}{\mathit{f}}_{\mathit{u}}$$

where A_s is the effective steel area (in the considered direction) and f_u is the ultimate tensile strength of the mesh steel. The corresponding nominal ultimate tensile stress of the ferrocement element is obtained by distributing this resultant over the gross section area (bh).

(2) $${\sigma }_t{}_u=\frac{{\mathit{T}}_{\mathit{u}}}{\mathit{b}\mathit{h}}=\frac{{\mathit{A}}_{\mathit{s}}{\mathit{f}}_{\mathit{u}}}{\mathit{b}\mathit{h}}$$

Where, ‘b’ and ‘h’ are the width and thickness of the Ferro cement element. Therefore, the stress-strain relationships of Ferro cement in direct tension and compression are as shown in Figure 5b.

Thus, Equation 2 is not an empirical assumption, but a force-equilibrium based expression representing the steel-controlled tensile capacity of a cracked ferrocement composite. The use of “effective steel area” also implicitly accounts for the fact that not all mesh wires may be fully mobilised depending on orientation, anchor-age, and cracking pattern, consistent with the cited ferrocement tension models.

In a Ferro cement element subjected to bending, the various layers of reinforcing mesh may be arranged in several different ways. (i.e. they may either be uniformly distributed throughout the cross section or be lumped together in the tension zone or both in tension and compression zones). In the present study, steel reinforcements are uniformly distributed throughout the cross-section of the element Figure 6a. When subjected to pure bending and as the applied moment approaches the ultimate value, the distribution of stress across the thickness will be as shown in Figure 6c. According to the assumed material behavior, the outer fibers will deform plastically, while the region near the neutral axis still remain elastic. At higher strains, the elastic core diminishes, the stress in the core then contribute very little to the resisting bending moment because of their short lever arm. Hence at collapse, the stress distribution as shown in Figure 6c may be assumed without unduly impairing the accuracy.

Figure 6
Stress block diagrams. (a) Section; (b) Strain; (c) Actual stresses; (d) Idealized stresses.

Figures 6b-d illustrate the transition from actual nonlinear strain and stress distributions to equivalent idealised stress blocks that satisfy force equilibrium and moment compatibility. Such idealised stress blocks are widely used in analytical and plastic analysis of ferrocement and fibre-reinforced cementitious composites to replace complex nonlinear stress fields with statically equivalent representations. The validity of these idealisations is indirectly verified in the present study through close agreement between analytically predicted flexural capacity and experimental test results. So, the idealised stress–strain relationships and stress blocks shown are force-equivalent representations of experimentally observed nonlinear behaviour and are adopted solely to facilitate analytical flexural strength prediction.

In Figure 6, Where ‘x’ is the depth of neutral axis at plastic collapse.

σ_cu = ultimate compressive strength of the matrix, which is equal to 0.67f_cu.

σ_tu = ultimate tensile strength of matrix as given in Equation 2.

C = Resultant compressive force

T = Resultant tensile force

(3) $$\text{C}={\text{σ}}_{\text{cu}}\text{bx}$$

(4) $$\text{T}={\text{σ}}_{\text{tu}}\text{b}\left(\text{h}-\text{x}\right)$$

The depth of neutral axis may be obtained from the consideration of equilibrium of forces in horizontal direction

i.e., Total Compression (C) = Total Tension (T).

The moment M_u at collapse is then obtained by taking moment of ‘T’ about the line of action of ‘C’ as

(5) $${\text{M}}_{\text{u}}={\text{σ}}_{\text{tu}}\text{b}\left(\text{h}-\text{x}\right)\text{h}/2$$

Table 2 shows a comparison of the test ultimate moments with the predicted ultimate bending strengths of the ferrocement specimens. From Table 2, it is noted that the predicted ultimate moments by the methods adopted herein shown good agreement with test results. The flexural strength of the ferrocement plates is determined by using strain compatibility and equilibrium equations (elastic theory) and plastic analysis approach. The average and standard deviation of ultimate theoretical moment to the ultimate experimental moment for elastic and plastic analysis theory are found to be 1.134, 0.1108 and 1.174 & 0.1306 respectively.

Table 2
Comparison of test data with theoretical predictions.

TEST SERIES	NO. OF LAYERS OF WIRE MESH	ULTIMATE MOMENT MTest (N–m)	MElastic N–m	MPlastic N–m	${\text{M}}_{\text{Elast}}/{\text{M}}_{\text{Test}}$	${\text{M}}_{\text{Plast}}/{\text{M}}_{\text{Test}}$
A0L	0L	50.276	51.718	51.718	1.029	1.029
A3L	3L	177.813	220.789	234.00	1.242	1.316
A4L	4L	232.988	286.683	288.315	1.230	1.237
A5L	5L	269.775	341.597	361.125	1.266	1.339
A6L	6L	300.438	390.200	408.956	1.299	1.361
B0L	0L	50.768	51.718	51.718	1.019	1.019
B3L	3L	206.01	220.798	234.00	1.072	1.136
B4L	4L	275.91	286.683	288.315	1.039	1.045
B5L	5L	322.260	341.597	361.125	1.060	1.121
B6L	6L	359.04	390.200	408.956	1.087	1.139
			Average		1.134	1.174
			Standard Deviation		0.1108	0.1306

• M_Elast: Moment of resistance calculated based on elastic theory.
• M_Plast: Moment of resistance calculated based on plastic analysis theory.

A comparison of test moments with theoretical ultimate moments is presented in Figures 7 and 8. From this comparison, it can be understood that both elastic (i.e. using strain compatibility and equilibrium equations) and plastic analysis methods fairly estimate the flexural strength of the ferrocement plate elements with ±10% accuracy. If the ferrocement composite of a given cross-section consists of a higher volume fraction of mesh reinforcement (mortar matrix part will decrease), the load carrying capacity and ductility of the composite will increase, since the main load sharing element in the ferrocement is mesh reinforcement. Ferrocement elements are skin elements, if these thin sections are reinforced with a greater number of layers of mesh wire, then such sections show similar behavior as steel section.

Figure 7
Comparison of M_Exp & M_pred w.r.t No. of layers of mesh.

Figure 8
Comparison of M_Exp & M_pred w.r.t No. of layers of mesh.

Therefore, the ultimate moments computed for plates with higher volume fraction of mesh reinforcements by elastic and particularly by plastic analysis theories are appropriate compared to plates consisting of less number of mesh layers. For the two series of specimens (A &B) the average ratios of the predicted to the calculated ultimate moments for the two methods are 1.134 and 1.174 respectively, with corresponding standard deviations of 0.11 and 0.13. Therfore, the proposed method i.e. plastic analysis theory to compute ultimate flexural resistance is satisfactory and it is much simpler than elastic (conventional reinforced concrete) theory method.

4. CONCLUSIONS

Based on experimental evaluations of ferrocement plate elements subjected to flexural loading, the following inferences have been derived:

1. Both the initial cracking moment and the ultimate moment capacity exhibit a positive correlation with the increase in the volume fraction of reinforcement.

2. Elevated volume fractions of reinforcement enhance the efficacy of crack width control.

3. The proposed methodology, employing plastic analysis principles, effectively predicts the flexural strength of ferrocement plate elements with satisfactory accuracy.

4. Increasing the volume fraction of mesh reinforcement yields a more pronounced enhancement in ultimate moment capacity relative to the cracking moment.

5. ACKNOWLEDGMENTS

I would like to express my sincere gratitude to the staff and administration of Acharya Nagarjuna University and Bapatla Engineering College.

6. BIBLIOGRAPHY

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Publication Dates

• Publication in this collection
  09 Mar 2026
• Date of issue
  2026

History

• Received
  06 Oct 2025
• Accepted
  27 Jan 2026