MIDAS Civil PSC Bridge Design: Prestress Loss, Tendon Profiling, and Stress Checks

MIDAS Civil PSC Bridge Design: Prestress Loss, Tendon Profiling, and Stress Checks

Prestressed concrete bridge design is one of my favorite topics — there's something satisfying about profiling tendons and watching the stress checks come out green. MIDAS Civil handles the full PSC workflow: tendon profiling, prestress loss calculation, and stress checks per AASHTO LRFD. Let me walk you through how I set up a PSC bridge design.

PSC Section Definition

Box Girder Section

1. Model > Section > PSC Section
2. Define box girder:
   • Top slab width: 12.0m
   • Top slab thickness: 250mm
   • Bottom slab width: 6.0m
   • Bottom slab thickness: 200mm (variable)
   • Web thickness: 400mm (two webs)
   • Total depth: 2.0m
   • Fillets: 300×300mm at web-slab junctions
3. Calculate section properties:
   • Area (A), Centroid (yc), Moment of inertia (Iy, Iz)
   • Section modulus (St = I/yc, Sb = I/(h-yc))

I-Girder Section

1. Model > Section > PSC Section > I-Beam
2. Define:
   • Top flange width: 500mm
   • Top flange thickness: 200mm
   • Web thickness: 200mm
   • Bottom flange width: 600mm
   • Bottom flange thickness: 300mm
   • Total height: 1800mm

Material Properties

1. Model > Material
2. Set:
   • Concrete (girder): f'c = 40 MPa, f'ci = 35 MPa (at transfer)
   • Concrete (deck): f'c = 30 MPa
   • Prestressing strand: fpu = 1860 MPa, fpy = 1674 MPa (0.9 × fpu)
   • Eps: 195,000 MPa
   • Rebar: fy = 420 MPa

Tendon Profiling

Tendon Layout

1. Load > Prestress > Tendon Profile
2. Define tendon profile:
   • Tendon type: Internal (bonded or unbonded) or external
   • Number of tendons: e.g., 12 tendons
   • Strands per tendon: e.g., 19 strands of 15.2mm diameter
   • Tendon area: Ap = 19 × 140 = 2660 mm² per tendon

Tendon Geometry

1. Define tendon path along the girder:
   • Harparabolic profile: Most common for continuous girders
   • Straight + harped: For simply supported girders
2. Set control points:
   • At supports: Tendon near top of section (negative moment region)
   • At midspan: Tendon near bottom of section (positive moment region)
3. Set eccentricity at each control point:
   • At support: e = +800mm (above centroid)
   • At midspan: e = -800mm (below centroid)
4. MIDAS Civil generates smooth tendon profile

Tendon Stressing

1. Load > Prestress > Stressing
2. Set:
   • Jacking stress: fpj = 0.75 × fpu = 1395 MPa
   • Stressing method: Pre-tensioned or post-tensioned
   • Stressing sequence: Both ends or one end
   • Anchorage set: Slip = 6mm (typical for post-tensioned)

Prestress Loss Calculation

Immediate Losses

Elastic Shortening (ES)

1. MIDAS Civil calculates:
   • ΔfpES = Ep × Δfc/Eci
   • Δfc: Change in concrete stress at tendon centroid due to prestress
   • Eci: Modulus at transfer (lower than final Ec)
2. For sequential stressing:
   • First tendon: Full elastic shortening loss
   • Last tendon: Zero elastic shortening loss
   • Average: 50% of full loss

Anchorage Set Loss

1. For post-tensioned tendons:
   • ΔfpAS = (ΔL × Ep) / L
   • ΔL: Anchorage slip (6mm typical)
   • L: Tendon length
2. Loss is highest at jacking end and decreases with distance

Friction Loss

1. For post-tensioned tendons:
   • ΔfpF = fpj × (1 - e^(-(μα + KL)))
   • μ: Curvature friction coefficient (0.25 for steel ducts)
   • α: Cumulative angle change (radians)
   • K: Wobble friction coefficient (0.0017 per meter)
   • L: Tendon length from jacking end

Long-Term Losses

Creep Loss (CR)

1. MIDAS Civil calculates:
   • ΔfpCR = Ep × εcreep = Ep × (φ(t,ta) × Δfc/Ec)
   • φ(t,ta): Creep coefficient per ACI 209 or CEB-FIP
   • Δfc: Sustained concrete stress at tendon level
2. Creep loss develops over years (50% in 1 year, 100% in 30 years)

Shrinkage Loss (SH)

1. MIDAS Civil calculates:
   • ΔfpSH = Ep × εshrinkage
   • εshrinkage: Per ACI 209 or CEB-FIP model
   • Typical: 200-400 × 10⁻⁶
2. Shrinkage loss develops over years

Relaxation Loss (RE)

1. MIDAS Civil calculates:
   • ΔfpRE = fpj × (log(t)/log(1000)) × RE_factor
   • RE_factor: 1.5% for low-relaxation strand (per AASHTO 5.9.5.3.2b)
   • t: Time in hours after stressing
2. Relaxation is relatively small (2-3% of fpj)

Total Prestress Loss

1. MIDAS Civil reports total loss per tendon:
   • Immediate: ES + AS + Friction
   • Long-term: CR + SH + RE
   • Total: Immediate + Long-term
2. Typical total loss: 15-25% of fpj
3. Effective prestress: fpe = fpj - Total Loss

Stress Checks

At Transfer (Initial)

1. Design > PSC Design > Stress Check > Transfer
2. Check concrete stresses immediately after transfer:
   • Compression (top): fc = Pi/Ag - Pi×e/St + Mdl/St
     • Limit: 0.60 × f'ci (per AASHTO 5.9.4.1.1)
   • Tension (bottom): ft = Pi/Ag + Pi×e/Sb - Mdl/Sb
     • Limit: 0.24 × √f'ci (without bonded reinforcement)
     • Limit: 0.58 × √f'ci (with bonded reinforcement)
3. If stresses exceed limits:
   • Increase section size
   • Reduce jacking stress
   • Add temporary support
   • Add reinforcement in tension zone

At Service (Final)

1. Design > PSC Design > Stress Check > Service
2. Check concrete stresses under full service loads:
   • Compression (top): fc = Pe/Ag - Pe×e/St + (Mdl + Mll)/St
     • Limit: 0.60 × f'c (per AASHTO 5.9.4.2.1)
   • Tension (bottom): ft = Pe/Ag + Pe×e/Sb - (Mdl + Mll)/Sb
     • Limit: 0.50 × √f'c (with bonded reinforcement and severe exposure)
     • Limit: 0.58 × √f'c (with bonded reinforcement and moderate exposure)
3. If stresses exceed limits:
   • Increase prestress force
   • Add more tendons
   • Increase section size
   • Add non-prestressed reinforcement

Decompression Check

1. For crack control:
   • Verify that tendon stress does not exceed decompression stress
   • Decompression: When concrete stress at tendon level reaches zero
   • fpe + Δfp (due to live load) ≤ fpy (yield stress of strand)

Ultimate Strength Design

Flexural Strength

1. Design > PSC Design > Flexural Strength
2. MIDAS Civil calculates:
   • Nominal moment (Mn):
     • For rectangular section: Mn = Aps × fps × (dp - a/2)
     • fps: Strand stress at ultimate (per AASHTO 5.7.3.1)
     • a: Depth of equivalent stress block
   • Factored moment (Mu): From load combinations
   • Check: φMn ≥ Mu
     • φ = 0.90 (tension-controlled)
     • φ = 0.75 (compression-controlled)

Shear Strength

1. Design > PSC Design > Shear Strength
2. MIDAS Civil calculates:
   • Concrete shear (Vc): Per AASHTO 5.8.3.3
     • Vc = 0.0316 × β × √f'c × bv × dv
     • β: Per AASHTO 5.8.3.4.2
   • Prestress contribution (Vp): Vertical component of tendon force
   • Stirrup shear (Vs): Vs = Av × fy × dv / s
   • Total: φVn = φ(Vc + Vp + Vs)
   • Check: φVn ≥ Vu

Tendon Stress Distribution

1. Results > Prestress > Tendon Stress
2. View stress along each tendon:
   • At jacking end: fpj (maximum)
   • Along tendon: Decreasing due to friction
   • At anchor end: fpj - friction loss
   • After all losses: fpe (effective prestress)
3. Verify all tendon stresses are within limits:
   • fpj ≤ 0.75 × fpu (jacking)
   • fpe ≥ 0.50 × fpu (after losses, minimum effective)

Camber and Deflection

Camber Calculation

1. Results > Prestress > Camber
2. MIDAS Civil calculates:
   • Immediate camber: Due to prestress force (upward)
   • Dead load deflection: Due to self-weight (downward)
   • Net camber: Prestress camber - dead load deflection
   • Long-term camber: Including creep multiplier (typically 2.0-3.0)
3. Use camber for:
   • Setting formwork elevation
   • Providing upward camber to compensate for long-term deflection

Long-Term Deflection

1. Results > Prestress > Long-Term Deflection
2. View deflection over time:
   • At transfer: Immediate (elastic)
   • At 1 year: Including 50% creep and 70% shrinkage
   • At 10 years: Including 90% creep and 95% shrinkage
   • At 30 years: Including 100% creep and 100% shrinkage
3. Check:
   • Total deflection: ≤ L/240 (typical for PSC bridges)
   • Live load deflection: ≤ L/800 (vehicular)

Wrapping Up

PSC bridge design in MIDAS Civil is comprehensive and well-organized. The thing I always emphasize: get your prestress losses right. The effective prestress after losses determines everything — stress checks, deflection, ultimate capacity. Don't just accept the default loss parameters; check them against your project's specifications. And always check stresses at transfer — that's when the concrete is youngest and weakest, and the prestress force is highest.