Pre-tensioned precast beam calculator — EN 1992-1-1 with the Dutch National Annex
Check a simply supported pre-tensioned precast beam with a rectangular, I, T or inverted-T section (for example a ledger beam whose bottom flange carries the floor slabs on both sides). Enter the span, the characteristic loads, the section, the concrete and the strands in up to three layers; the calculator follows the prestress from the bed to the final state.
It works out the relaxation in the bed, the loss by elastic shortening at transfer and the time-dependent losses from creep, shrinkage and relaxation, then checks the concrete stresses at transfer and in service, the ultimate bending resistance by strain compatibility, shear with the prestress and the camber and deflection. The Dutch National Annex values are used throughout.
Open this example in the calculator →
What it checks
- Stress limits at tensioning and after transfer (EN 1992-1-1 §5.10.2.1, §5.10.3)
- Losses: relaxation, elastic shortening, creep, shrinkage (§5.10.4–§5.10.6, §3.3.2, Annex B)
- Transmission length of the strands (§8.10.2.2)
- Concrete stresses at transfer and in service, uncracked check under the frequent combination (§5.10.2.2, §7.2, §7.3)
- Bending resistance by strain compatibility (§6.1) and shear with the prestress (§6.2.2, §6.2.3)
- Camber and deflection (§7.4, EN 1990 A1.4.3 with NB limits)
Scope
- One simply supported span; up to 10 loads (uniform, partial, point).
- Rectangle, I, T and inverted-T sections (gross concrete section).
- Straight, fully bonded 7-wire strands in up to three layers; stirrups optional.
Not covered (the calculator says NOT COVERED instead of approximating)
- Deflected or debonded strands, post-tensioning, continuous beams.
- Ordinary longitudinal reinforcement, composite topping, lifting, transport and erection stages.
- Cracked members under the frequent combination (a factor in the Dutch crack-control rule is not yet transcribed): the beam must stay uncracked.
- The flanges themselves (shear between web and flange §6.2.4, hanger reinforcement, flange bending) and torsion: loads act on the beam axis, so a beam loaded from one side needs these checked separately.
- Minimum reinforcement and the check against brittle failure.
- Fatigue and fire.
Worked example
A single span of 12.0 m on two pinned supports, carrying 12 kN/m permanent and 10 kN/m imposed load (category B, offices) plus self-weight. I-section h = 900 mm (top flange 500 × 150, web 160, bottom flange 400 × 200), C50/60, cement class R, RH 70 %, exposure XC1; 14 strands Ø12.5 (8 at 50 mm, 4 at 100 mm, 2 at 850 mm) tensioned to 1350 MPa, released gradually after 1 day at f_ck(t) = 35 MPa; stirrups Ø8 at 300 mm.
Inputs
| Input | Value |
|---|---|
| Section shape | I |
| Total height h | 900 mm |
| Web width b_w (rectangle: width) | 160 mm |
| Top flange width (I, T) | 500 mm |
| Top flange thickness (I, T) | 150 mm |
| Bottom flange width (I, inverted T) | 400 mm |
| Bottom flange thickness (I, inverted T) | 200 mm |
| Concrete strength class | C50/60 |
| Cement class (S slow, N normal, R rapid) | R |
| Relative humidity of the environment | 70 % |
| Exposure class (governing) | XC1 |
| Strand nominal diameter Ø | 12.5 mm |
| Area per strand (product data) | 93 mm² |
| Tensile strength f_pk (product data) | 1860 MPa |
| 0.1 % proof stress f_p0,1k (product data) | 1640 MPa |
| Stress at tensioning σ_pi | 1350 MPa |
| Layer 1: number of strands | 8 |
| Layer 1: height above the bottom | 50 mm |
| Layer 2: number of strands | 4 |
| Layer 2: height above the bottom | 100 mm |
| Layer 3: number of strands | 2 |
| Layer 3: height above the bottom | 850 mm |
| Age of the concrete at transfer | 1 days |
| f_ck at transfer from tests (blank = §3.1.2) | 35 MPa |
| Release of the strands | gradual |
| Stirrups: diameter (blank = none) | 8 mm |
| Stirrups: number of legs | 2 |
| Stirrups: spacing | 300 mm |
Main steps
| Step | Clause | Working | |
|---|---|---|---|
| Max sagging moment span 1 | EN 1992-1-1 §5.4 | M_Ed,1 = envelope max (6.10b, Q on all spans) = x = 6 m = 660.4 kNm | |
| Shear force at support 1 (axis) | EN 1992-1-1 §5.4; 6.2.1(8) | V_Ed,s1 = envelope max |V| at the support axis = x = 0 m = 220.1 kN | |
| Shear force at support 2 (axis) | EN 1992-1-1 §5.4; 6.2.1(8) | V_Ed,s2 = envelope max |V| at the support axis = x = 12 m = 220.1 kN | |
| Concrete strength at transfer (from tests) | EN 1992-1-1 §3.1.2(5) | f_ck,t = input (tests) = 35 = 35 MPa | |
| Stress at tensioning | EN 1992-1-1 §5.10.2.1(1) (NB) | σ_pi / σ_p,max = σ_pi / σ_p,max ≤ 1.0 = 1350 / 1476 = 0.9146 | PASS ⚠ |
| Prestress force after transfer | EN 1992-1-1 §5.10.3 | P_m0 = P_0 − A_p · Δσ_el = 1.748e+06 − 1302 · 64.23 = 1664 kN | |
| Prestress after transfer | EN 1992-1-1 §5.10.3(2) (NB) | σ_pm0 / σ_pm0,max = σ_pm0 / σ_pm0,max ≤ 1.0 = 1278 / 1394 = 0.9169 | PASS ⚠ |
| Final creep coefficient φ(∞, t_0) | EN 1992-1-1 §Annex B.1, Eq. (B.2) | φ_0 = φ_RH · β_fcm · β_t0 = 1.264 · 2.206 · 0.7045 = 1.964 | |
| Final total shrinkage | EN 1992-1-1 §3.1.4(6), Eq. (3.8) | ε_cs = ε_cd,∞ + ε_ca,∞ = 0.0003734 + 0.0001 = 0.0004734 | |
| Time-dependent losses (creep, shrinkage, relaxation) | EN 1992-1-1 §5.10.6(2), Eq. (5.46) | Δσ_p,c+s+r = (ε_cs·E_p + 0.8·Δσ_pr + E_p/E_cm·φ·σ_c,QP) / (1 + E_p/E_cm·A_p/A_c·(1 + A_c·z_cp²/I_c)·(1 + 0.8·φ)) = (0.0004734·195000 + 0.8·47.1 + 195000/37278·1.964·7.926) / (1 + 195000/37278·1302/2.43e+05·(1 + 2.43e+05·281²/2.301e+10)·(1 + 0.8·1.964)) = 186.7 MPa | |
| Final prestress force | EN 1992-1-1 §5.10.6 | P_m,∞ = P_m0 − A_p · Δσ_p,c+s+r = 1.664e+06 − 1302 · 186.7 = 1421 kN | |
| Transmission length, upper value (ULS: shear, anchorage) | EN 1992-1-1 §8.10.2.2(3), Eq. (8.18) | l_pt2 = 1.2 · l_pt = 1.2 · 633.3 = 759.9 mm | |
| Compression at transfer (end of l_pt1) | EN 1992-1-1 §5.10.2.2(5) | σ_c / σ_c,lim,t = σ_c / σ_c,lim,t ≤ 1.0 = 15.84 / 21 = 0.7541 | PASS ⚠ |
| Top tension at transfer (end of l_pt1) | EN 1992-1-1 §7.1(2) | σ_ct / f_ctm,t = σ_ct / f_ctm,t ≤ 1.0 = 1.766 / 3.21 = 0.55 | PASS ⚠ |
| Compression at transfer (midspan) | EN 1992-1-1 §5.10.2.2(5) | σ_c / σ_c,lim,t = σ_c / σ_c,lim,t ≤ 1.0 = 14.01 / 21 = 0.6669 | PASS ⚠ |
| Top tension at transfer (midspan) | EN 1992-1-1 §7.1(2) | σ_ct / f_ctm,t = σ_ct / f_ctm,t ≤ 1.0 = 0.01065 / 3.21 = 0.003316 | PASS ⚠ |
| Crack control: uncracked (frequent) | EN 1992-1-1 §7.3.1, Table 7.1N (NB) | σ_ct / f_ctm = σ_ct / f_ctm ≤ 1.0 = 0 / 4.072 = 0 | PASS ⚠ |
| Bending resistance | EN 1992-1-1 §6.1(2)–(5); strain compatibility | M_Rd = Σ F_p · (d − z_c) = strain compatibility = 1244 kNm | |
| Deflection span 1 (appearance) | EN 1990 §A1.4.3 (NB) | w_qp / w_lim = w_qp / (0.004 · l) ≤ 1.0 = 6.582 / (0.004 · 1.2e+04) = 0.1371 | PASS ⚠ |
| Deflection span 1 (additional, frequent) | EN 1990 §A1.4.3 (NB) | w_add,freq / w_lim = w_add,freq / (0.003 · l) ≤ 1.0 = 1.253 / (0.003 · 1.2e+04) = 0.03481 | PASS ⚠ |
| Bending span 1 | EN 1990 §6.4.2(3), Eq. (6.8) | M_Ed / M_Rd = M_Ed / M_Rd ≤ 1.0 = 660.4 / 1244 = 0.5308 | PASS ⚠ |
| Shear support 1 | EN 1990 §6.4.2(3), Eq. (6.8) | V_Ed / V_Rd = V_Ed / V_Rd ≤ 1.0 = 220.1 / 273.2 = 0.8058 | PASS ⚠ |
| Shear support 2 | EN 1990 §6.4.2(3), Eq. (6.8) | V_Ed / V_Rd = V_Ed / V_Rd ≤ 1.0 = 220.1 / 273.2 = 0.8058 | PASS ⚠ |
| Shear at the end of l_pt2 | EN 1990 §6.4.2(3), Eq. (6.8) | V_Ed / V_Rd = V_Ed / V_Rd ≤ 1.0 = 187.1 / 273.2 = 0.685 | PASS ⚠ |
Outcome
PASS — all checks satisfied ⚠
- 1 span (12 m) on pinned – pinned supports; I 900 mm, C50/60, 14 strands Ø12.5 (P_m0 1664 kN → P_m,∞ 1421 kN).
- 3 characteristic loads, combined with EN 1990 6.10a/6.10b (CC2, use category B) in 4 load cases.
- Governing: Prestress after transfer — 1278.1 MPa demand against 1394.0 MPa capacity, unity check 0.92 (OK).
- All 13 checks pass.
- 1 warning — see below.
| Result | Value |
|---|---|
| UC Stress at tensioning | 0.9146 |
| UC Prestress after transfer | 0.9169 |
| UC Compression at transfer (end of l_pt1) | 0.7541 |
| UC Top tension at transfer (end of l_pt1) | 0.55 |
| UC Compression at transfer (midspan) | 0.6669 |
| UC Top tension at transfer (midspan) | 0.003316 |
| UC Crack control: uncracked (frequent) | 0 |
| UC Deflection span 1 (appearance) | 0.1371 |
| UC Deflection span 1 (additional, frequent) | 0.03481 |
| UC Bending span 1 | 0.5308 |
| UC Shear support 1 | 0.8058 |
| UC Shear support 2 | 0.8058 |
| UC Shear at the end of l_pt2 | 0.685 |
| Governing UC | 0.9169 (Prestress after transfer) |
| P_m0 | 1664 kN |
| P_m,∞ | 1421 kN |
| M_Rd | 1244 kNm |
Dutch National Annex values used
| Symbol | Value | Clause | Status |
|---|---|---|---|
| ψ0 | 0.5 | EN 1990 Table NB.2 – A1.1 (NB) | transcribed ⚠ |
| γ_G,sup | 1.35 | EN 1990 Table NB.4 – A1.2(B) (NB) | transcribed ⚠ |
| γ_Q,1 | 1.5 | EN 1990 Table NB.4 – A1.2(B) (NB) | transcribed ⚠ |
| γ_G,sup | 1.2 | EN 1990 Table NB.4 – A1.2(B) (NB) | transcribed ⚠ |
| γ_Q,1 | 1.5 | EN 1990 Table NB.4 – A1.2(B) (NB) | transcribed ⚠ |
| ψ1 | 0.5 | EN 1990 Table NB.2 – A1.1 (NB) | transcribed ⚠ |
| ψ2 | 0.3 | EN 1990 Table NB.2 – A1.1 (NB) | transcribed ⚠ |
| C_max | C90/105 | EN 1992-1-1 3.1.2(2)P (NB) | transcribed ⚠ |
| α_cc | 1 | EN 1992-1-1 3.1.6(1)P (NB) | transcribed ⚠ |
| γ_C | 1.5 | EN 1992-1-1 2.4.2.4(1), Table 2.1N (NB) | transcribed ⚠ |
| γ_S | 1.15 | EN 1992-1-1 2.4.2.4(1), Table 2.1N (NB) | transcribed ⚠ |
| k1 | 0.8 | EN 1992-1-1 5.10.2.1(1)P (NB) | transcribed ⚠ |
| k2 | 0.9 | EN 1992-1-1 5.10.2.1(1)P (NB) | transcribed ⚠ |
| k7 | 0.75 | EN 1992-1-1 5.10.3(2) (NB) | transcribed ⚠ |
| k8 | 0.85 | EN 1992-1-1 5.10.3(2) (NB) | transcribed ⚠ |
| Annex B | Informative | EN 1992-1-1 Bijlage B (NB) | transcribed ⚠ |
| α_ct | 1 | EN 1992-1-1 3.1.6(2)P (NB) | transcribed ⚠ |
| r_sup | 1 | EN 1992-1-1 5.10.9(1)P (NB) | transcribed ⚠ |
| r_inf | 1 | EN 1992-1-1 5.10.9(1)P (NB) | transcribed ⚠ |
| k2 | 0.45 | EN 1992-1-1 7.2(3) (NB) | transcribed ⚠ |
| w_max | Reinforcement + bonded prestressing: w_max ≤ 0.30 mm; bonded prestressing only: ∆σ_p ≤ ξ 275 MPa. Both: frequent combination. mm; MPa | EN 1992-1-1 7.3.1(5), Table 7.1N (NB) | transcribed ⚠ |
| γ_P,fav | 1 | EN 1992-1-1 2.4.2.2(1) (NB) | transcribed ⚠ |
| f_yk,max | 600 MPa | EN 1992-1-1 3.2.2(3)P (NB) | transcribed ⚠ |
| ν | 0.6*(1 - fck/250) | EN 1992-1-1 6.2.2(6) (NB) | transcribed ⚠ |
| ν1 | nu | EN 1992-1-1 6.2.3(3) (NB) | transcribed ⚠ |
| α_cw | 1 (non-prestressed); 1 + sigma_cp/fcd for 0 < sigma_cp <= 0.25 fcd; 1.25 for 0.25 fcd < sigma_cp <= 0.5 fcd; 2.5*(1 - sigma_cp/fcd) for 0.5 fcd < sigma_cp < 1.0 fcd | EN 1992-1-1 6.2.3(3) (NB) | transcribed ⚠ |
| cot θ_min | 1 | EN 1992-1-1 6.2.3(2) (NB) | transcribed ⚠ |
| cot θ_max | 2.5 | EN 1992-1-1 6.2.3(2) (NB) | transcribed ⚠ |
| w_max/l | 0.004 fraction of l_rep | EN 1990 A1.4.3(4) (NB) | transcribed ⚠ |
| w_add/l | 0.003 fraction of l_rep | EN 1990 A1.4.3(3) (NB) | transcribed ⚠ |
| l_rep | l_rep = 2 × cantilever length | EN 1990 A1.4.3(3) (NB) | transcribed ⚠ |
Clauses used in the worked example
EN 1990 §6.4.2(3), Eq. (6.8), EN 1990 §6.4.3.2, Eq. (6.10a), Table A1.2(B) (NB), EN 1990 §6.4.3.2, Eq. (6.10b), Table A1.2(B) (NB), EN 1990 §6.5, EN 1990 §6.5.3(2)a, Eq. (6.14b) (NB), EN 1990 §6.5.3(2)b, Eq. (6.15b), EN 1990 §6.5.3(2)c, EN 1990 §6.5.3(2)c, Eq. (6.16b), EN 1990 §A1.4.3 (NB), EN 1991-1-1 §Table A.1 (prestressed concrete 25 kN/m³), EN 1991-1-1 §characteristic value (input), EN 1992-1-1 §3.1.2(5), EN 1992-1-1 §3.1.2, Table 3.1, EN 1992-1-1 §3.1.2, Table 3.1 (NB), EN 1992-1-1 §3.1.3(3), Eq. (3.5), EN 1992-1-1 §3.1.3, Table 3.1, EN 1992-1-1 §3.1.4(5), Annex B.1, EN 1992-1-1 §3.1.4(6), Eq. (3.10), EN 1992-1-1 §3.1.4(6), Eq. (3.12), EN 1992-1-1 §3.1.4(6), Eq. (3.8), EN 1992-1-1 §3.1.4(6), Table 3.3, EN 1992-1-1 §3.1.6(1)P (NB), EN 1992-1-1 §3.1.6(2); 8.10.2.2(1) (NB), EN 1992-1-1 §3.1.7(3), Eq. (3.19), EN 1992-1-1 §3.1.7(3), Eq. (3.21), EN 1992-1-1 §3.1.7, Table 3.1, EN 1992-1-1 §3.2.2, Annex C (NB), EN 1992-1-1 §3.2.7(2) (NB), EN 1992-1-1 §3.3.2(7), Eq. (3.29), EN 1992-1-1 §3.3.6(3), EN 1992-1-1 §3.3.6(6) (NB), EN 1992-1-1 §5.10.2.1(1) (NB), EN 1992-1-1 §5.10.2.1(1), Eq. (5.41) (NB), EN 1992-1-1 §5.10.2.2(5), EN 1992-1-1 §5.10.3, EN 1992-1-1 §5.10.3(2) (NB), EN 1992-1-1 §5.10.3(2), Eq. (5.43) (NB), EN 1992-1-1 §5.10.4(1), EN 1992-1-1 §5.10.4(1), Eq. (5.44), EN 1992-1-1 §5.10.4–5.10.6, EN 1992-1-1 §5.10.6, EN 1992-1-1 §5.10.6(2), EN 1992-1-1 §5.10.6(2), Eq. (5.46), EN 1992-1-1 §5.10.8(2); 6.1(2) (NB), EN 1992-1-1 §5.10.9(1) (NB), EN 1992-1-1 §5.4, EN 1992-1-1 §5.4; 6.2.1(8), EN 1992-1-1 §6.1(2)–(5); strain compatibility, EN 1992-1-1 §6.2.1, EN 1992-1-1 §6.2.2(1), EN 1992-1-1 §6.2.2(6), Eq. (6.6N) (NB), EN 1992-1-1 §6.2.3(1), EN 1992-1-1 §6.2.3(2) (NB limits) (NB), EN 1992-1-1 §6.2.3(3), EN 1992-1-1 §6.2.3(3) (NB), EN 1992-1-1 §6.2.3(3), Eq. (6.8), EN 1992-1-1 §6.2.3(3), Eq. (6.9), EN 1992-1-1 §7.1(2), EN 1992-1-1 §7.2, EN 1992-1-1 §7.3.1, Table 7.1N (NB), EN 1992-1-1 §7.4.3; 3.1.4, EN 1992-1-1 §7.4.3; 5.10, EN 1992-1-1 §7.4.3; EN 1990 A1.4, EN 1992-1-1 §8.10.2.2(1), Eq. (8.15), EN 1992-1-1 §8.10.2.2(2), Eq. (8.16), EN 1992-1-1 §8.10.2.2(3), Eq. (8.17), EN 1992-1-1 §8.10.2.2(3), Eq. (8.18), EN 1992-1-1 §Annex B.1, EN 1992-1-1 §Annex B.1 (NB), EN 1992-1-1 §Annex B.1, Eq. (B.2), EN 1992-1-1 §Annex B.1, Eq. (B.9), EN 1992-1-1 §Annex B.2, Eq. (B.11), EN 1992-1-1 §Annex B.2, Eq. (B.12) (NB)
Join free during the pilot
Cvil is in its pilot period. Leave your email address and we'll keep you posted on news and any offers once we officially start.
Just your email address, no card needed.