This educational application supplements, but does not replace, the official AASHTO LRFD Bridge Design Specifications, applicable state DOT manuals, project specifications, and professional engineering judgment.

Full-bridge designer

One model, deck to pile tip

Change the girder spacing, the slab thickness or the limit state and every downstream demand re-solves: deck strip moments, distribution factors, girder flexure and shear, bearing reactions, pier-cap strut-and-tie, column P-Δ interaction and the foundation. Each check cites its AASHTO LRFD article and reports a utilization ratio.

Limit-state selector — AASHTO 3.4.1

Basic gravity combination with the design vehicular live load.

γDC / γDW / γLL / γEQ

1.25 / 1.5 / 1.75 / 0

Governing check

Pier-cap shear

AASHTO 5.7.3.3 — ratio 0.861

Checks passing

12 / 12

Design lanes / MPF

3 / 0.85

Table 3.6.1.1.2-1

Load path

Traffic & environmental loadsAASHTO 3
Deck slab, haunch & barriersAASHTO 9
Live-load distributionAASHTO 4.6.2.2
Girders / superstructureAASHTO 5 · 6
Bearing reactionsAASHTO 14.7
Pier cap · columns · abutmentsAASHTO 5.8.2 · 11
Foundations — piles / footingsAASHTO 10

Superstructure geometry

Span LftNumber of spans—Deck width (out-to-out)ftClear roadwayftNumber of girders—Girder spacing SftDeck overhangftSlab thickness tₛinHaunchinWearing surfaceinBarrier weight (each)klfSkewdeg

Girder

Girder typeGirder self weightklfGirder depthinKg (long. stiffness)in⁴FyksiFlange area (each)in²Web areain²Deck f'cksiGirder f'cksify (reinforcement)ksi

Substructure

Cap widthinCap depthinCap cantileverftNumber of columns—Column diameterinColumn clear heightftLongitudinal steel ratio—Effective length factor k—

Foundation & environment

Foundation typePiles per pier—Pile diameterinEmbedded lengthftUnit skin friction qsksfUnit tip resistance qpksfPile spacing× DDesign scour depthftSeismic coefficient Csm—Response modification R—

Stage 1AASHTO LRFD 3.5 / 3.6

Traffic & permanent loads

Component dead load split into the non-composite stage DC1 and the composite stage DC2, the wearing-surface load DW, and the HL-93 vehicular live-load envelope on a single loaded lane.

Slab w

1.0094 klf

(tₛ/12)·0.150·S

Haunch w

0.0375 klf

18 in wide haunch

Girder self weight

0.3100 klf

Barrier share

0.2080 klf

2 barriers ÷ N girders

w_DC1 (non-composite)

1.3569 klf

girder + slab + haunch

w_DC2 (composite)

0.2080 klf

barriers / superimposed DL

w_DC total

1.5649 klf

w_DW per girder

0.3325 klf

§3.5.1 future overlay

M_DC1 = w_DC1·L²/8

2442.4 k-ft

bare girder carries it

M_DC2 = w_DC2·L²/8

299.5 k-ft

composite section

M_DW

478.8 k-ft

M_LL+IM (distributed)

2261.0 k-ft

V_DC1

81.4 kip

V_DC2

12.5 kip

V_DW

20.0 kip

V_LL+IM

116.3 kip

M_u = γ_DC(M_DC1 + M_DC2) + γ_DW·M_DW + γ_LL·M_LL+IM = 1.25(2442.4 + 299.5) + 1.5(478.8) + 1.75(2261.0) = 8102.4 k-ft

γ·M_DC1

3053.0 k-ft

γ·M_DC2

374.4 k-ft

γ·M_DW

718.2 k-ft

Factored design moment M_u

8102.4 k-ft

Detailing sketchSimple-span moment diagram — DC1, DC2, DW and LL+IM

M_DC1 = 2442 k-ft (girder + slab + haunch on the non-composite section) · M_DC2 = 300 k-ft (barriers on the composite section) · M_DW = 479 k-ft · M_LL+IM = 2261 k-ft (distributed) · factored M_u = 8102 k-ft.

Truck moment (no IM)

1883.2 k-ft

critical rear-axle spacing 14 ft

Tandem moment

1450.4 k-ft

Lane moment (0.64 klf)

1152.0 k-ft

HL-93 envelope M

3656.7 k-ft/lane

truck + lane, IM = 33 %

Truck shear

66.4 kip

Tandem shear

49.2 kip

Lane shear

38.4 kip

HL-93 envelope V

126.7 kip/lane

Stage 2AASHTO LRFD 9.7.3 / A4

Deck slab & barriers

Equivalent-strip live-load moment, factored strip demand and the transverse reinforcement check over the interior girders.

M_LL strip

7.65 k-ft/ft

((S+2)/32)·P·IM

M_DC strip

0.96 k-ft/ft

wS²/10 continuity

M_u strip

15.06 k-ft/ft

As required

0.517 in²/ft

d = 7.19 in

Deck flexure — φMn ≥ Mu (strip method)

AASHTO LRFD 9.7.3 / A40.417

demand 15.06 k-ft/ft / resistance 36.10 k-ft/ft — OK

#5 @ 6 in top mat, As,req = 0.517 in²/ft.

Detailing sketchDeck slab — section, plan and longitudinal section

Top mat #4 @ 4.5 in (A_s = 0.533 in²/ft) for the negative strip moment over the girders; bottom mat #4 @ 6.0 in for the positive strip moment between girders. Required A_s = 0.517 in²/ft at M_u = 15.06 k-ft/ft. Distribution steel and 2 in clear top / 1 in clear bottom cover per AASHTO 5.10.1 and 9.7.3.

Stage 3AASHTO LRFD 4.6.2.2.2 / 4.6.2.2.3

Live-load distribution

Approximate distribution equations for a concrete deck on steel or prestressed I-girders, interior and exterior, with the skew correction on moment.

Kg / (12·L·tₛ³)

3.6185

g_M interior

0.7598

one / two+ lanes enveloped

g_M exterior

0.7729

e = 1.017, dₑ = 2.25 ft

g_M design

0.7729

g_V interior

0.9180

g_V exterior

0.9180

Skew correction

1.0000

§4.6.2.2.2e

g_V design

0.9180

Stage 4AASHTO LRFD 6.10.7.1

Steel composite girder

Factored moment and shear demand on the controlling girder against the composite flexural and web shear resistance.

M_DC1 (non-composite)

2442.4 k-ft

M_DC2 (composite)

299.5 k-ft

M_DW

478.8 k-ft

M_LL+IM (distributed)

2261.0 k-ft

γ·M_DC1 + γ·M_DC2

3427.4 k-ft

γ·M_DW

718.2 k-ft

γ·M_LL+IM

3956.8 k-ft

Factored design moment M_u

8102.4 k-ft

Girder flexure — φMn ≥ Mu

AASHTO LRFD 6.10.7.10.631

demand 8102.35 k-ft / resistance 12845.34 k-ft — OK

PNA in the steel section.

V_DC1

81.4 kip

V_DC2

12.5 kip

V_DW

20.0 kip

V_u

350.9 kip

Girder shear — φVn ≥ Vu

AASHTO LRFD 6.10.9.20.779

demand 350.85 kip / resistance 450.23 kip — OK

Detailing sketchComposite steel plate girder — section, elevation and framing plan

Effective flange width b_eff = min(S, L/4, 12tₛ) = 8.50 ft (AASHTO 4.6.2.6). PNA in the steel section.

Stage 5AASHTO LRFD 14.7.6

Bearings & load transfer

Girder end reactions delivered to the substructure, and the service compressive stress on the elastomeric pad.

R_DC

103.3 kip

R_DW

21.9 kip

R_LL+IM

116.3 kip

R_u (factored)

365.6 kip

Bearing service compressive stress

AASHTO LRFD 14.7.6.3.20.732

demand 0.91 ksi / resistance 1.25 ksi — OK

Detailing sketchElastomeric bearing — section and plan

22 × 12 in pad, 5 elastomer layers with steel shims. Service reaction 242 kip gives σ_s = 0.915 ksi against the 1.25 ksi limit (AASHTO 14.7.6.3.2) — adequate.

Stage 6AASHTO LRFD 5.8.2 / 11.6

Pier cap — sectional & strut-and-tie

Cap flexure and shear from the bearing point loads, plus the D-region strut-and-tie model at the cap cantilever.

Cap self weight

7.200 klf

Cap span (c/c columns)

11.33 ft

M_u cap

1182.8 k-ft

a/d ratio

0.63

Deep member — STM required

Pier-cap flexure

AASHTO LRFD 5.6.30.339

demand 1182.80 k-ft / resistance 3487.54 k-ft — OK

Top mat detailed as 6 #11 (As = 9.36 in²); flexure requires 3.17 in², the STM tie 5.92 in².

Pier-cap shear

AASHTO LRFD 5.7.3.30.861

demand 982.26 kip / resistance 1140.22 kip — OK

Strut inclination θ

55.2 deg

Limiting strut stress f_cu

3.400 ksi

§5.8.2.5.3

Strut Pn

4113 kip

Tie Pn = fy·Ast

505 kip

STM compression strut

AASHTO LRFD 5.8.2.50.136

demand 560.57 kip / resistance 4112.64 kip — OK

a/d = 0.63 < 2 — deep-beam behaviour, STM required.

STM tension tie

AASHTO LRFD 5.8.2.40.633

demand 319.75 kip / resistance 505.44 kip — OK

Strut inclination θ = 55.2°.

Detailing sketchPier cap — elevation, section and plan

6 #11 continuous top bars (A_s = 9.36 in²) with skin and bottom steel; #5 double-leg stirrups @ 6 in through the cap. Cap 72 in wide × 96 in deep, 5.00 ft cantilever each end, 4 columns at 11.33 ft centres.

Stage 7AASHTO LRFD 5.6.4 / 4.7.4

Pier columns — axial, slenderness & seismic

Accumulated axial load, the moment magnifier for slenderness, and the seismic shear carried into the column under Extreme Event I.

P_DC

383 kip

P_LL

291 kip

P_u

1070 kip

φPn

4902 kip

kℓ/r

50.4

Slender — magnification applies

Euler load Pc

6398 kip

Magnifier δ

1.287

Seismic shear / column

17.5 kip

Csm/R = 0.056

Column axial–moment interaction

AASHTO LRFD 5.6.4.50.594

demand 0.59 — / resistance 1.00 — — OK

Pu = 1070 kip, Mu = 826 k-ft, δ = 1.287 (slender: kℓ/r > 22).

Detailing sketchPier column — section and elevation

22 #10 longitudinal bars (A_st = 27.94 in², ρ = 1.54 %) against the required A_st = 27.14 in² at ρ = 1.50 %. #4 spiral at 3 in pitch, 2 in clear cover. Design actions P_u = 1070 kip, M_u = 826 k-ft (AASHTO 5.6.4, 5.10.4.2).

Stage 8AASHTO LRFD 10.7.3

Deep foundation — driven pile group

Skin friction and tip resistance with scour-reduced embedment, group efficiency, and the factored demand per pile.

Skin friction Qs

322 kip

Tip resistance Qp

106 kip

Factored QR per pile

193 kip

Demand per pile

146 kip

Single-pile factored axial resistance

AASHTO LRFD 10.7.3.80.757

demand 145.83 kip / resistance 192.76 kip — OK

Qs = 322 kip, Qp = 106 kip, φ = 0.45 (static analysis).

Pile-group resistance

AASHTO LRFD 10.7.3.90.757

demand 1312.50 kip / resistance 1734.84 kip — OK

Group efficiency η = 1.00 at 3D spacing.

Embedment below design scour

AASHTO LRFD 2.6.4.4.20.175

demand 10.00 ft / resistance 57.00 ft — OK

8.0 ft of skin friction neglected within the scour prism.

Detailing sketchPile group — cap plan, pile elevation and cap section

9 piles at 3.0D centres, 18 in diameter, 57 ft embedded with the top 8 ft inside the scour prism neglected. Demand 146 kip/pile against φQ_n = 193 kip (AASHTO 10.7.3.8).

Stage 9AASHTO LRFD 1.3.2

Utilization summary

Every limit-state check in the cascade with its AASHTO article and demand-to-resistance ratio. The governing item is the one nearest to — or beyond — unity.

Deck flexure — φMn ≥ Mu (strip method)

AASHTO LRFD 9.7.3 / A40.417

demand 15.06 k-ft/ft / resistance 36.10 k-ft/ft — OK

#5 @ 6 in top mat, As,req = 0.517 in²/ft.

Girder flexure — φMn ≥ Mu

AASHTO LRFD 6.10.7.10.631

demand 8102.35 k-ft / resistance 12845.34 k-ft — OK

PNA in the steel section.

Girder shear — φVn ≥ Vu

AASHTO LRFD 6.10.9.20.779

demand 350.85 kip / resistance 450.23 kip — OK

Bearing service compressive stress

AASHTO LRFD 14.7.6.3.20.732

demand 0.91 ksi / resistance 1.25 ksi — OK

Pier-cap flexure

AASHTO LRFD 5.6.30.339

demand 1182.80 k-ft / resistance 3487.54 k-ft — OK

Top mat detailed as 6 #11 (As = 9.36 in²); flexure requires 3.17 in², the STM tie 5.92 in².

Pier-cap shear

AASHTO LRFD 5.7.3.30.861

demand 982.26 kip / resistance 1140.22 kip — OK

STM compression strut

AASHTO LRFD 5.8.2.50.136

demand 560.57 kip / resistance 4112.64 kip — OK

a/d = 0.63 < 2 — deep-beam behaviour, STM required.

STM tension tie

AASHTO LRFD 5.8.2.40.633

demand 319.75 kip / resistance 505.44 kip — OK

Strut inclination θ = 55.2°.

Column axial–moment interaction

AASHTO LRFD 5.6.4.50.594

demand 0.59 — / resistance 1.00 — — OK

Pu = 1070 kip, Mu = 826 k-ft, δ = 1.287 (slender: kℓ/r > 22).

Single-pile factored axial resistance

AASHTO LRFD 10.7.3.80.757

demand 145.83 kip / resistance 192.76 kip — OK

Qs = 322 kip, Qp = 106 kip, φ = 0.45 (static analysis).

Pile-group resistance

AASHTO LRFD 10.7.3.90.757

demand 1312.50 kip / resistance 1734.84 kip — OK

Group efficiency η = 1.00 at 3D spacing.

Embedment below design scour

AASHTO LRFD 2.6.4.4.20.175

demand 10.00 ft / resistance 57.00 ft — OK

8.0 ft of skin friction neglected within the scour prism.