The Prestressed Concrete tool handles the design and analysis of prestressed concrete members, covering prestress losses, service-level stress checks at transfer and final conditions, and flexural strength verification at the strength limit state. Both pretensioned and post-tensioned members are supported.

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Pretensioned members have the tendons stressed before the concrete is cast. The prestress is transferred to the concrete by bond after the concrete reaches sufficient strength (typically at 70–75% of f'_c). Precast bridge beams (AASHTO-PCI girders, box beams) are usually pretensioned.

Post-tensioned members are cast with ducts in place; the tendons are stressed after the concrete has hardened and then anchored at the ends of the member. Post-tensioning is common in cast-in-place bridge decks, segmental bridges, and building transfer beams. The tool handles both systems, with distinct prestress loss calculations for each.

The initial prestress f_si (strand stress at jacking) is reduced by losses before reaching the effective prestress f_pe at service conditions. Losses fall into two categories:

Immediate losses (at transfer or stressing):

• Elastic shortening — as the prestress is applied, the concrete shortens elastically, reducing the strand elongation. For pretensioned members, ES = (E_s / E_c) × f_cir, where f_cir is the concrete stress at the tendon centroid immediately after transfer.
• Friction and wobble (post-tensioned) — tendon friction against the duct and unintended angular change cause stress to decrease along the member length from the jacking end.
• Anchorage set (post-tensioned) — a small amount of strand slippage occurs when the anchor wedges seat, causing a local stress drop near the anchorage.

Time-dependent losses:

• Creep — sustained compressive stress in the concrete causes continuing deformation over time, which reduces the prestress. Creep losses depend on the concrete mix, member age at loading, and ambient humidity.
• Shrinkage — as concrete dries and cures, it contracts, shortening the member and reducing the tendon strain.
• Relaxation — high-strength prestressing steel under sustained tension loses stress over time. Low-relaxation strand (the most common type) limits this loss to approximately 1–2% of the initial prestress.

Total losses for typical prestressed concrete bridge members range from 15% to 25% of the initial jacking stress. The tool computes these losses per the AASHTO LRFD Bridge Design Specifications or ACI 318 refined method, depending on the selected code.

Prestressed concrete is typically designed to remain uncracked at service loads, so stress checks control the design. Two loading stages must be checked:

At transfer (release) — the prestress P_i is applied before most dead loads are in place. With only the member self-weight acting, the top fiber may be in tension and the bottom fiber in high compression. The allowable transfer stress limits are (per ACI 318 and AASHTO):

• Compression: 0.60 × f'_ci (concrete strength at transfer)
• Tension: 3√f'_ci (psi) without bonded reinforcement, higher with it

At final service — the effective prestress P_e after all losses acts together with the full dead and live load. The stress at any fiber in the cross-section is:

f = −P_e/A ± P_e × e × y / I ∓ M × y / I

where e is the eccentricity (distance from centroid to tendon), y is the distance from the centroid to the fiber being checked, and the signs account for whether the fiber is above or below the centroid.

At the strength limit state, the nominal flexural capacity of a prestressed beam is:

M_n = A_ps × f_ps × (d_p − a/2)

where f_ps is the stress in the prestressing steel at nominal strength (typically close to f_pu, the ultimate tensile strength of the strand), and a is the equivalent rectangular stress block depth. The tool computes f_ps using the AASHTO or ACI 318 approximate expression and verifies φM_n ≥ M_u.

Consider a simply supported 12 in × 24 in rectangular pretensioned beam, L = 30 ft, with:

• A_ps = 4 × 0.153 = 0.612 in² (four 0.5 in diameter low-relaxation strands)
• f_pe = 150 ksi (effective prestress after losses)
• P_e = 0.612 × 150 = 91.8 kips
• Eccentricity at midspan: e = 8 in (strands 4 in from bottom of 24 in beam)
• Section properties: A = 288 in², I = 13,824 in⁴, y_b = y_t = 12 in

Self-weight moment at midspan:

w = (12 × 24 / 144) × 0.150 = 0.300 klf
M_g = 0.300 × 30² / 8 = 33.75 kip·ft = 405 kip·in

Bottom fiber stress at midspan (after superimposed service load M_s = 800 kip·in):

f_bot = −P_e/A + P_e × e × y_b / I − M × y_b / I
f_bot = −91.8/288 + 91.8 × 8 × 12 / 13,824 − (405 + 800) × 12 / 13,824
f_bot = −0.319 + 0.641 − 1.046 = −0.724 ksi (compression ✓)

The tool performs all of these calculations automatically and flags any stress that exceeds the allowable limits.

• Always check both the transfer and service conditions — a beam that satisfies service stresses may still overstress the concrete at transfer when the full prestress is applied with only self-weight acting.
• Increasing the number of strands raises the prestress force but also increases the eccentricity effects. Sometimes reducing the eccentricity (raising the strand profile) is more effective than adding strands.
• For multi-span continuous prestressed bridges, the secondary (hyperstatic) moments from post-tensioning must be included in the stress checks. The tool provides input fields for secondary moment terms.
• Check minimum reinforcement (M_cr requirements) to ensure the beam has adequate reserve capacity after cracking, even if service stresses remain below cracking limits.

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