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FRP rebar and strengthening

Design · closed form · rectangular section

A rectangular FRC or concrete beam reinforced with steel bars or with non-metallic bars (GFRP, BFRP, CFRP, AFRP) and strengthened with an externally bonded FRP laminate. Same closed-form engine as the hybrid module. Steel bars yield and harden; non-metallic bars are linear elastic to rupture; the laminate ruptures or debonds.

Formulation and limit states. Patel, D. D., Pleesudjai, C., Neithalath, N., and Mobasher, B. (2026). Limit-state based design of hybrid reinforced UHPC flexural beams using parametric modeling. Engineering Structures, 357, 122353. doi:10.1016/j.engstruct.2026.122353

What you need

  • Beam span, section, cover, bar sizes and counts, loading arrangement.
  • The matrix laws, imported from an inverse-analysis workbook or typed.
  • The bar properties: for steel the modulus, yield strength, ultimate stress and ultimate strain; for a non-metallic bar the modulus and tensile strength.
  • The laminate properties: width, ply thickness, number of plies, modulus, tensile strength, the substrate strain at bonding and, if used, a debonding strain limit.

Step 1 · Geometry

Geometry tab

Geometry tab. Module defaults. The laminate is drawn under the section and along the soffit.
  1. Span, width and height.
  2. Plastic length, with the suggested value.
  3. Cover and bars. Cover to the bar center, diameter and count of the top and bottom FRP bars. A count of 0 removes the layer.
  4. Loading and load spacing.
  5. Drawings. Bars in green, the laminate in purple with its width and total thickness printed.

Step 2 · Matrix laws

The Tension Model and Compression Model tabs and the Import Material button are identical to those of the Hybrid beam module.

Step 3 · Bars

Reinforcement Model tab

Reinforcement Model tab. Shown for non-metallic bars, linear elastic to rupture.

The Bar Type list at the top of the tab selects the bar law. Both laws run through the same section solver; the list only changes which numbers you type.

  1. Bar law. Non-metallic bars: modulus \(E_f\) and tensile strength \(f_{fu}\); the rupture strain is computed. Steel bars: modulus \(E_s\), yield strength \(f_{sy}\), ultimate stress \(f_{su}\) and ultimate strain \(\varepsilon_{su}\) (a fraction, 0.05 is 5 percent); \(f_{su} = f_{sy}\) gives a flat plateau.
  2. Derived values. Non-metallic: the rupture strain in percent and the modular ratio \(n = E_f/E\). Steel: the yield strain \(f_{sy}/E_s\), the hardening ratio \(f_{su}/f_{sy}\) and \(n = E_s/E\).
  3. The plot. A straight line to rupture, or a yield plateau with a hardening branch. Drag the vertices to change the law; for steel the end point also moves along the strain axis.

Limit states follow the bar type: Bottom Bar Rupture for a non-metallic bar; Bottom Steel Yield and Bottom Steel Ultimate, plus the service stress at 0.8 \(f_{sy}\), for steel. The report and the output workbook carry the same names.

Step 4 · FRP laminate

FRP Laminate tab

FRP Laminate tab. An externally bonded laminate at the soffit.
  1. Laminate properties. Width \(b_f\), thickness per ply \(t_f\), number of plies, modulus \(E_f\), tensile strength \(f_{fu}\), the substrate strain at the time of bonding (the strain already in the soffit from self weight when the laminate is applied), and the debonding strain limit. Enter 0 for the debonding limit to let rupture govern.
  2. Once the laminate is lost. What the analysis does after rupture or debonding: stop, or continue with the bars and fibers alone.
  3. Derived values. Laminate area, reinforcement ratio, modular ratio, the strain ratio at bonding and the limiting laminate strain with the mechanism that governs it.
  4. The plot. The laminate law offset by the substrate strain at bonding.

Step 5 · Update Results and read the limit states

Moment-Curvature tab

Moment-Curvature tab.
  1. Limit states. First crack, FRP engaged (the laminate starts carrying stress once the substrate strain at bonding is exceeded), FRP rupture or debonding, compression yield, and the bar states: rupture for a non-metallic bar, yield and ultimate for steel.
  2. Their values in the text box.

The Moment-Strain, Load-Deflection, Stress Profile and Force Profile tabs work as in the Hybrid beam module. The Force Profile shows the laminate force as a bar at the soffit.

Step 6 · Export and save

Export Report, Download Output Data and File → Save work as in every module.