Grade 500 Bar Substitution in a 7.5 m Transfer Beam
A simply supported transfer beam spans 7.5 m with b = 350 mm, h = 650 mm, effective depth 590 mm and f'c = 28 MPa. The design uses 4-#25 bottom bars (fy = 420 MPa, 510 mm² each) and #10 two-legged stirrups at 300 mm; analysis gives Mu = 380 kN·m and Vu = 210 kN at the critical section. The beam is a gravity member in an ordinary, non-seismic frame. Because Grade 420 bars are unavailable, the contractor proposes to substitute 3-#25 Grade 500 bars, arguing that 3 × 510 mm² at 500 MPa gives 765 kN of yield force against 857 kN for the original, and that the higher grade 'more than compensates' while reducing congestion in the 350 mm web. The bars are straight and terminate in 500 mm square columns where the available embedment is 480 mm; the #25 Grade 420 development length was computed as 620 mm and a standard 90° hook is detailed.
1. Compute the flexural capacity of the original design and of the proposed substitution, and decide whether the substitution can be approved on strength grounds.
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Original design. a = As fy /(0.85 f'c b) = (2040 × 420)/(0.85 × 28 × 350) = 856,800/8,330 = 102.9 mm. Mn = 856,800 × (590 − 51.4) = 461 kN·m, so φMn = 0.9 × 461 = 415 kN·m ≥ 380 kN·m. Utilisation is 92% - the beam has little spare capacity.
Proposed substitution. a = (1530 × 500)/8,330 = 91.8 mm. Mn = 765,000 × (590 − 45.9) = 416 kN·m, so φMn = 0.9 × 416 = 375 kN·m.
Result: 375 < 380 kN·m, short by about 1.3%. The beam fails flexure, marginally but definitively. Ductility is not the issue: c = 91.8/0.85 = 108 mm, εt = 0.003 × (590 − 108)/108 = 0.013, comfortably tension-controlled.
Why the contractor's reasoning fails. The yield-force ratio (765/857 = 0.89) is the wrong comparison. Capacity depends on As fy times the lever arm, and removing a bar also reduces the internal lever arm slightly; the product of the two losses is what pushes the section below the demand.
2. Assuming a 4-#25 Grade 500 substitution were adopted, list and explain the additional checks required beyond flexural strength.
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Tension-controlled behaviour. Recheck c/d and εt ≥ 0.005 with the new fy and confirm As stays below the maximum for a tension-controlled section; higher-grade steel can push a heavily reinforced section toward the compression-controlled region.
Development. ℓd scales approximately with fy, so the straight development length grows from 620 mm to roughly 740 mm (about 19%), and the hooked length ℓdh grows correspondingly. With only 480 mm of embedment the hook must be verified with its cover and confinement factors, not assumed adequate.
Shear. Vc depends on f'c and the section, not on the longitudinal fy, but Vs uses the actual stirrup fy. If Grade 500 stirrups are also substituted, Vs rises and the upper limit Vs ≤ 0.66√f'c bw d must be checked.
Serviceability. Recheck deflection and crack width; with the same bar area and a higher yield strength, service steel stress falls slightly, but the change must be shown, not assumed.
Detailing and material. Confirm the Grade 500 bar's ductility and bendability, that lap lengths are updated throughout, and that seismic provisions do not apply - if this were a special moment frame, over-strength would raise joint shear and column demands and a simple swap would be unacceptable.
3. What would you recommend to the contractor, and what would have to be verified for that recommendation?
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Recommendation: 3-#29 Grade 500. As = 3 × 645 = 1935 mm². a = (1935 × 500)/8,330 = 116.1 mm. Mn = 967,500 × (590 − 58.1) = 515 kN·m, so φMn = 463 kN·m ≥ 380 kN·m, with 22% reserve, which also restores the margin the original design had. Ductility is fine: c = 136.6 mm, εt = 0.003 × (590 − 136.6)/136.6 = 0.010, tension-controlled.
Why this works better than 4-#25 Grade 500. Three larger bars fit in one layer in the 350 mm web (clear spacing roughly 82 mm, greater than db and well above the minimum), so the effective depth is preserved and congestion is actually reduced - which was the contractor's real objective.
What must be verified.
- Development of #29 bars into the 500 mm column, including the hook, since ℓd grows with both fy and bar size.
- Shear capacity with the actual stirrup grade, and the stirrup spacing against the d/2 limit.
- Deflection and crack control at service load.
- Written approval of the substitution by the designer of record, with the revised bar mark and lap details issued as a drawing revision - not a site instruction.