Tutorial 5: Simple Span Adjacent Box Beam Bridge U.S. Units) (LRFD) Selected Hand Calculation

This design example demonstrates the design of a 100-ft. single-span AASHTO Type BIV-48 box beam bridge with no skew. This example illustrates in detail the design of a typical interior beam at the critical sections for positive flexure, shear and deflection due to prestress, dead loads and live load. The superstructure consists of eight beams butted together as shown in 1, Bridge Cross-Section . A 3-inch bituminous surfacing will be placed on the beams as a wearing surface. Design live load is HL-93. The design is carried out in accordance with the AASHTO LRFD Bridge Design Specifications, Sixth Edition, 2012.

FIGURE 1. Bridge Cross-Section

MATERIALS

Precast Beams:

AASHTO Type BIV-48 Box Beam, as shown in Figure 19, AASHTO Type BIV-48 Box Beam.

FIGURE 2. AASHTO Type BIV-48 Box Beam

Concrete strength at release f`_ci = 4.5 ksi

Concrete strength at 28 Days f`_c = 5.5 ksi

Concrete unit weight w_c = 0.150 kcf

Overall beam length = 101.0 ft.

Design span = 100.0 ft.

Prestressing strands:

1/2 diameter, seven-wire, low relaxation

Area of one strand = 0.153 in²

Ultimate strength = 270.0 ksi

Yield strength, f_py = 0.9 f_pu= 243.0 ksi [LRFD Table 5.4.4.1-1]

Stress limits for prestressing strands [LRFD Table 5.9.3-1]

Before transfer $f_{p i} \leq 0.75 f_{p u} = 202.5 k s i$

At service limit state (after all losses) $f_{p e} \leq 0.8 f_{p y} = 194.4 k s i$

Modulus of elasticity E_p = 28500 ksi [LRFD Art. 5.4.4.2]

Reinforcing bars:

Yield strength, f_y = 60.0 ksi

Modulus of elasticity = 29000 ksi [LRFD Art. 5.4.3.2]

Bituminous surfacing:

Weight = 0.140 kcf [LRFD Table 3.5.1-1]

New Jersey type barrier:

Weight = 0.300 kip/ft./side

CROSS-SECTIONAL PROPERTIES, TYPICAL INTERIOR BEAM

b = effective flange width = 48 in. [LRFD Art. 4.6.2.6.1]

A = area of cross section of precast beam = 843 in²

h = overall depth of precast beam = 42 in

I = moment of inertia about the centroid of the non-composite precast beam = 203086 in²

y_b = distance from centroid to the extreme bottom fiber of the non-composite precast beam = 20.78 in

y_t = distance from centroid to the extreme top fiber of the non-composite precast beam = 21.22 in

S_b = section modulus for the extreme bottom fiber of the non-composite precast beam = 9773 in³

S_t = section modulus for the extreme top fiber of the non-composite precast beam = 9571 in³

Weight = 0.878 kip/ft.

E_{c} = 3300 {0 (0.150)}^{1.5} \sqrt{{f `}_{c}}

[LRFD Eq. 5.4.2.4-1]

Modulus of elasticity at release is

E_{c i} = 3300 {0 (0.150)}^{1.5} \sqrt{4.5} = 4066.840 k s i

Modulus of elasticity at service loads is

E_{c} = 3300 {0 (0.150)}^{1.5} \sqrt{5.5} = 4496.060 k s i

SHEAR FORCES AND BENDING MOMENTS

STRAND PATTERN

PRESTRESS LOSSES [LRFD INTERIMS 2005 - APPROXIMATE METHOD, ART.5.9.5]

TOTAL LOSSES AT SERVICE LOADS

CHECK CONCRETE STRESSES AT TRANSFER (RELEASE)

CHECK CONCRETE STRESSES AT SERVICE LOADS

CHECK OF STRENGTH LIMIT STATE

LIMITS OF REINFORCEMENT

Shear Design

PRETENSIONED ANCHORAGE ZONE [LRFD ART. 5.10.10]

DEFLECTION AND CAMBER

Parent topic: Hand Calculation for Selected Items