TSC Standards Series · Part 4 of 9

Reinforced Concrete Design per TS 500:2000

Complete design procedures for reinforced concrete beams, columns, and slabs per TS 500:2000 — flexural design with the rectangular stress block, shear design including the concrete contribution V_cr, column axial-bending interaction, cover requirements by exposure class, development length, and a step-by-step worked example.

Flexural Design — Beams and Slabs
Shear Design
Column Design — Axial and Bending
Concrete Cover — Exposure Classes
Development and Lap Splice Length
Worked Example — Rectangular Beam
Comparison: TS 500 vs ACI 318 vs EN 1992

1. Flexural Design — Beams and Slabs (TS 500 §8)

TS 500 uses a rectangular equivalent stress block with depth equal to 0.8 times the neutral axis depth x, and intensity equal to the design concrete compressive strength f_cd.

TS 500 §8.1 — Flexural Capacity

TS 500M_d = 0.8 · f_cd · b · x · (d − 0.4x)N·mm

TS 500A_s · f_yd = 0.8 · f_cd · b · x (force equilibrium)

Solving these two equations simultaneously for a given M_d gives the required steel area A_s. The neutral axis depth x is found from equilibrium, and the moment capacity is then checked.

Neutral Axis Limit — x_u,max/d

TS 500 §8.1 limits the relative neutral axis depth to ensure ductile flexural failure (steel yields before concrete crushes):

TS 500 §8.1.2 — Maximum Neutral Axis Depth

TS 500x_u,max/d = ε_cu / (ε_cu + ε_yd)

B420Cε_yd = 365/200000 = 0.001825 → x_u,max/d = 0.003/(0.003+0.001825) = 0.622

B500Cε_yd = 435/200000 = 0.002175 → x_u,max/d = 0.003/(0.003+0.002175) = 0.580

TSC seismic override: For beams in High ductility frames, TSC 2018 §7.4.2 further limits x/d ≤ 0.25 at potential plastic hinge zones, far more restrictive than TS 500's limit. This ensures significant steel yielding and large plastic rotations before concrete crushing.

Minimum and Maximum Steel Ratio

TS 500 §8.1.4 — Reinforcement Ratio Limits

Minρ_min = max(0.8·f_ctd/f_yd ; 0.002) for beams

Maxρ_max = 0.85 · β₁ · (f_cd/f_yd) · (x_u,max/d)

Where β₁ = 0.85 for f_ck ≤ 30 MPa, reducing by 0.05 per 5 MPa above 30 MPa (minimum 0.65). For C30/37 with B500C: ρ_max ≈ 0.85 × 0.85 × (20/435) × 0.580 ≈ 0.019 (1.9%).

T-Beam Effective Width

For beams integral with floor slabs, TS 500 §8.2 defines an effective flange width b_eff. The lesser of the following governs:

1/5 of the span length + web width b_w
Half the clear distance to adjacent beam + b_w
Actual slab overhangs on each side

2. Shear Design (TS 500 §8.3)

TS 500 uses a combined diagonal tension approach where the concrete provides a baseline shear resistance V_cr, and stirrups carry the remainder up to a maximum V_max.

TS 500 §8.3 — Shear Capacity

TS 500V_r = V_cr + V_w ≥ V_d

ConcreteV_cr = 0.65 · f_ctd · b_w · dN

StirrupsV_w = (A_sw/s) · f_ywd · dN (vertical stirrups)

MaxV_max = 0.22 · f_cd · b_w · dcrushing limit

Where A_sw = area of shear reinforcement legs crossing the critical section; s = stirrup spacing; f_ywd = design yield strength of stirrups. The design shear force V_d is taken at the critical section d from the face of support for uniform loads.

Minimum Shear Reinforcement

TS 500 §8.3.5 — Minimum Stirrup Requirement

Minρ_sw = A_sw/(b_w·s) ≥ 0.3·f_ctd/f_ywd

Maxs_max = min(d/2 ; 300 mm) for V_d ≤ V_cr

Maxs_max = min(d/4 ; 150 mm) for V_d > V_cr (TSC §7.4.4 seismic)

Seismic shear amplification: TSC 2018 §7.4.4 requires that the design shear in beams within the seismic force-resisting system be computed from the probable moment capacities at beam ends (capacity design), not from the linear analysis shear. This "capacity shear" can be 1.5–2× larger than the elastic analysis shear for slender beams.

3. Column Design — Axial and Bending (TS 500 §10)

TS 500 §10 covers short and slender columns under combined axial compression and biaxial bending. The interaction is checked using the equilibrium equations for the cross-section.

TS 500 §10.1 — Concentric Compression Capacity

TS 500N_d,max = 0.85 · f_cd · A_c + f_yd · A_sN

For combined axial and bending (P-M interaction), TS 500 requires explicit section analysis or interaction diagrams (abak). The general approach is to iterate neutral axis depth for equilibrium between N_d and M_d.

TSC 2018 Axial Load Limits for Columns (§7.3.1)

TSC 2018 §7.3.1 — Normalized Axial Load Limit

DTS 1/2n_d = N_d / (A_c · f_ck) ≤ 0.40

DTS 3/4n_d = N_d / (A_c · f_ck) ≤ 0.50

This limit ensures the column has sufficient ductility capacity. Highly axially loaded columns experience brittle crushing without yielding in the transverse reinforcement, so TSC caps the normalized axial load to maintain seismic ductility. Note that f_ck (not f_cd) is used in this check — it is a dimensionless demand-to-capacity ratio.

Strong Column — Weak Beam (§7.3.2)

TSC 2018 §7.3.2 — Column-Beam Moment Capacity Ratio

TSCΣM_ra,col ≥ 1.2 · ΣM_rk,beam

The sum of probable flexural capacities of columns framing into the joint (M_ra) must be at least 1.2 times the sum of probable flexural capacities of beams. This capacity design requirement ensures plastic hinges form in beams, not columns, producing a ductile sway mechanism.

Confinement Zones

TSC 2018 §7.3.4 defines confinement zones at the ends of columns where closely spaced transverse reinforcement is required:

Zone length: l_c = max(h_k ; l_n/6 ; 500 mm) where h_k = column cross-section dimension in the direction of bending, l_n = clear story height
Hoop spacing: s ≤ min(b_k/3 ; 100 mm ; 8φ_l,min) within confinement zone
Outside confinement zone: s ≤ min(b_k/2 ; 200 mm ; 12φ_l,min)

4. Concrete Cover — Exposure Classes (TS 500 Table 11)

Exposure Class	Environment Description	Min. Cover (mm)	Min. Concrete
XC1	Dry or permanently wet (indoors, foundations in non-aggressive ground)	25	C20/25
XC2	Wet, rarely dry (foundation in contact with soil)	30	C25/30
XC3	Moderate humidity (exterior sheltered, interior high humidity)	35	C25/30
XC4	Cyclic wet and dry (exterior exposed)	40	C30/37
XD1	Moderate humidity, chloride exposure (car parks, coastal indirect)	40	C35/45
XD2	Wet, chloride exposure (swimming pools, industrial)	45	C35/45
XS1	Exposed to airborne salt, not in direct contact with sea water	45	C35/45
XS2/3	Permanently submerged / tidal, splash zone (marine)	50	C40/50

These values represent the minimum concrete cover c_min. TS 500 §12.3 adds a tolerance allowance Δc_dev = 10 mm for normal construction quality, so the nominal cover (as specified on drawings) is c_nom = c_min + 10 mm.

5. Development and Lap Splice Length (TS 500 §9)

TS 500 §9.2 — Basic Development Length

TS 500l_b = (φ · f_yd) / (4 · f_bd)mm

TS 500f_bd = 2 · f_ctd (ribbed bars, good bond conditions)

The required development length l_d = α · l_b, where α accounts for bar position, coating, transverse reinforcement, and spacing. For standard bottom bars with good bond conditions, α = 1.0. For top bars (horizontal bars with > 300 mm concrete cast below), TS 500 requires α = 1.3.

Bar Diameter	l_b (mm) — B500C in C25/30	l_b (mm) — B500C in C30/37
φ 10	453	380
φ 12	543	456
φ 16	724	608
φ 20	905	760
φ 25	1131	950
φ 32	1448	1216

Lap splice lengths for Class 1 splices (≤ 25% of bars spliced within l_b) equal the development length l_d. For Class 2 splices (> 25% of bars spliced), l_lap = 1.3 · l_d per TS 500 §9.3. In seismic zones, TSC 2018 §7.4.2 prohibits lapping within the beam plastic hinge zone.

6. Worked Example — Rectangular Beam Design

Example: Office Beam — Flexure and Shear per TS 500

Given: Simply-supported beam, span L = 6.0 m, bw = 300 mm, h = 600 mm, d = 550 mm. Concrete C30/37 (f_ck = 30 MPa, f_cd = 20 MPa, f_ctd = 1.33 MPa). Steel B500C (f_yd = 435 MPa). Design moment M_d = 280 kN·m. Design shear V_d = 130 kN.

Step 1 — Flexure: Neutral Axis Depth
From equilibrium: A_s·f_yd = 0.8·f_cd·b·x → x = A_s·435 / (0.8·20·300)
Substituting into moment equation: 280×10⁶ = 0.8·20·300·x·(550 − 0.4x)
Solving: 280×10⁶ = 4800x(550 − 0.4x) → 4800x·550 − 4800·0.4·x² = 280×10⁶
2640000x − 1920x² = 280×10⁶ → x = 117.6 mm

Step 2 — Check neutral axis limit:
x_u,max/d = 0.003/(0.003 + 0.00218) = 0.580 → x_u,max = 0.580 × 550 = 319 mm
x = 117.6 mm < 319 mm ✓ (ductile section)

Step 3 — Required steel area:
A_s = 0.8·20·300·117.6 / 435 = 1301 mm²
Use 3φ25 (A_s,prov = 1473 mm²) ✓

Step 4 — Check minimum steel:
ρ_min = max(0.8×1.33/435 ; 0.002) = max(0.00245 ; 0.002) = 0.00245
A_s,min = 0.00245 × 300 × 550 = 404 mm² < 1473 mm² ✓

Step 5 — Shear design:
V_cr = 0.65 × 1.33 × 300 × 550 = 142.6 kN
V_d = 130 kN < V_cr = 142.6 kN → Only minimum stirrups required!
V_max = 0.22 × 20 × 300 × 550 = 726 kN ≫ V_d ✓
Provide φ8/200 (A_sw/s = 2×50/200 = 0.503 mm²/mm) — check minimum: 0.3×1.33/435 = 0.00092 → A_sw/(b_w·s) = 0.503/300 = 0.00168 ≥ 0.00092 ✓

Result: Beam 300×600, 3φ25 bottom bars, φ8 stirrups at 200 mm spacing. Full development length for B500C in C30/37: l_b = φ·f_yd/(4·f_bd) = 25×435/(4×2×1.33) = 1022 mm → use 1100 mm into supports.

7. Comparison: TS 500 vs ACI 318 vs EN 1992

Design Aspect	TS 500:2000	ACI 318-25	EN 1992-1-1
Stress block depth	0.8x (rectangular)	β₁·c (rectangular)	0.8x (for f_ck≤50)
Stress block intensity	f_cd	0.85·f'_c	η·f_cd (η=1 for ≤50)
Max strain ε_cu	0.003	0.003	0.0035
Concrete shear (beams)	V_cr = 0.65·f_ctd·b·d	V_c = 0.17λ√f'_c·b·d (simplified, new §22.5)	V_Rd,c = [0.12k(100ρ·f_ck)^1/3]·b·d
Shear reinforcement	V_w = (A_sw/s)·f_ywd·d (vertical)	V_s = (A_v/s)·f_yt·d	V_Rd,s = (A_sw/s)·z·f_ywd·cotθ
Column axial limit (seismic)	n_d ≤ 0.40 (DTS1/2, TSC §7.3.1)	P_u/(A_g·f'_c) ≤ 0.20 for special frames	ν_d = N_Ed/(A_c·f_cd) limit by EC8 §5.4
Strong col / weak beam	ΣM_ra,col ≥ 1.2·ΣM_rk,beam	ΣM_nc ≥ 1.2·ΣM_nb	ΣM_Rc,col ≥ 1.3·ΣM_Rb,beam
Development length basis	l_b = φ·f_yd/(4·f_bd)	l_d = (3f_y/(40λ√f'_c))·(ψ_tψ_eψ_s/(c_b/d_b+K_tr/d_b))·d_b	l_bd = α_1..6·l_b,rqd where l_b,rqd=φ·σ_sd/(4·f_bd)

RC Beam Calculator → RC Column Calculator → Next: Steel Design →

Preliminary design only. All formulas reference TS 500:2000 and TSC 2018. Verify the applicable edition and any amendments with the project's licensed structural engineer before use in construction documents.

← Previous Load Combinations & Safety Factors Next → Steel Design — TS 648 / TS EN 1993

Reinforced Concrete Design per TS 500:2000

Contents

1. Flexural Design — Beams and Slabs (TS 500 §8)

Neutral Axis Limit — xu,max/d

Minimum and Maximum Steel Ratio

T-Beam Effective Width

2. Shear Design (TS 500 §8.3)

Minimum Shear Reinforcement

3. Column Design — Axial and Bending (TS 500 §10)

TSC 2018 Axial Load Limits for Columns (§7.3.1)

Strong Column — Weak Beam (§7.3.2)

Confinement Zones

4. Concrete Cover — Exposure Classes (TS 500 Table 11)

5. Development and Lap Splice Length (TS 500 §9)

6. Worked Example — Rectangular Beam Design

7. Comparison: TS 500 vs ACI 318 vs EN 1992

Related Tools & Guides

Neutral Axis Limit — x_u,max/d