Page 186 - Bridge and Highway Structure Rehabilitation and Repair

CHAPTER 4 AN ANALYTICAL APPROACH TO FRACTURE AND FAILURE 161

Euler method of incremental loads: This method deals with first order or mild nonlinear

problems. Select small increments in loads in the post-linear load deflection stage until conver-
gence is reached.
Newton-Raphson (N-R) Method: For a higher degree of nonlinearity, the N-R Method is
used. Derivatives of nonlinear terms are solved with linear terms. It is more accurate than the
incremental load method since second order method is used.
4.10.3 Procedures for Analysis

1. Non-composite analysis cannot be combined with composite analysis. The two conditions
need to be evaluated separately.
2. For LRFD construction load combination cases, construction processes cannot be superposed,
and separate analysis for each construction stage needs to be carried out.
Temporary construction loads of machinery and materials need to be considered, with

the bridge performing only at its partial strength. In the final stage, multiple longitudinal
joints need to be filled up with cast in place closure pours, which changes the strength of

the superstructure.
3. The order of load application shall be consistent with that on an actual bridge, i.e., dead
load stages followed by live loads, etc. This procedure is particularly important for slab and
beam bridges using accelerated bridge construction and precast construction techniques.
4. Various stages of an unfinished bridge need to be modeled mathematically, with boundary

conditions representing partial composite action. AASHTO code currently does not address
the sequence, construction loads, or design methods of joints.
5. Mathematical modeling also applies to timber and metal formwork sheeting and temporary
column supports to girders and deck slabs during construction. Strength of three-dimen-
sional pipe assemblies or individual props needs to be evaluated. Overstress from materials
and machinery loads, local buckling of pipe columns, temporary footing settlement, and
unexpected lack of performance of temporary connections have led to many collapses and
construction deaths in the past.

4.11 SINGLE SPAN LIVE LOAD ANALYSIS

4.11.1 Moving HL-93 Truckloads on a Single Span

The author has developed simplified expressions for maximum moments, their location,
maximum shears, and reactions for design based on moving HS-20 truckload.
Combined HL-93 truck and lane loads:

1. Weight of HS-20 Truck 3 72 kips used with additional lane load of 0.64 kips/ft.
2. Weight of alternate tandem truck 3 50 kips used with additional lane load of 0.64 kips/ft.

A comparison between an HS-20 truck and an alternate tandem truck shows that up to a
40-foot span, tandem truck moments are highest.

For spans 9 40 ft but : 150 ft span, HS-20 truckloads are highest.
For spans 9 150 ft, lane load is higher. Lane load is combined with tandem truck for spans
up to 40 ft and with HS-20 truckloads for spans 9 40 ft.
Maximum shear/support reactions are, in all cases, highest for HS-20 trucks for spans up
to 210 ft.
For spans 9 210 ft, lane load shear is highest.
Theorem: Maximum live load BM occurs when the mid-span section divides the distance
between the center of gravity of three axle loads and the adjacent wheel load equally.