The usual procedure followed by most designers in preliminary designs of bridges involves
the following steps:
1. Preliminary layout of structure
2. Preliminary design of floor system and calculation of weights and dead load
3. Preliminary layout of bracing systems and estimates of weights and loads
4. Preliminary estimate of weight of main load-bearing structure
5. Preliminary stress analysis
6. Check of initial assumptions for dead load
Preliminary Weight of Arch. The ratios given in Art. 14.6 can guide designers in making a preliminary layout with nearly correct proportions. The 16 examples of arches in Art. 14.8 also can be helpful for that purpose and, in addition, valuable in making initial estimates of??weights and dead loads.
Equations (14.1) and (14.2), shown graphically in Fig. 14.33, were developed to facilitate estimating weights of main arch members.
For a true arch of low-alloy, high-strength steel (without ties), the ratio R of weight of rib to total load on the arch may be estimated from
R = 0.032 + 0.000288S
where S span, ft.
For a tied arch of low-alloy, high-strength steel, the ratio R of weight of rib and tie to
total load on the arch may be estimated from
R = 0.088 + 0.000321S
This equation was derived from a study of seven of the structures in Art. 14.8 that are tied arches made of low-alloy, high-strength steels predominantly for ribs, trusses, and ties. Equation (14.1), however, is not supported by as many examples of actual designs and may give values on the high side for truss arches. Despite the small number of samples, both equations should give reasonably accurate estimates of weight for preliminary designs and cost estimates of solid-ribbed and truss arches and for comparative studies of different types of structures.
With R known, the weight W, lb per ft, of arch, or arch plus tie, is given by
where D dead load on arch, lb per ft, excluding weight of arch, or arch plus tie and L equivalent live load plus impact, lb per ft, on arch when the structure is fully loaded. D is determined from preliminary design of bridge components other than arches and ties.
Effect of Type of Steel on Arch Weights. The following approximate analysis may be used to determine the weight of arch rib or arch rib and tie based on the weight of arch for some initial design with one grade of steel and an alternative for some other grade with different physical properties.
Let Fb basic unit stress for basic design, ksi
Fa basic unit stress for alternative design, ksi
D dead load, lb per ft, excluding weight of rib, or rib and tie
L equivalent live load plus impact, lb per ft, for fully loaded structure
Wb weight of rib, or rib and tie, lb per ft for basic design
Wa weight of rib, or rib and tie, lb per ft, for alternate design
Pb total load, lb, carried by 1 lb of rib, or 1 lb of rib and tie, for basic design
Pa total load, lb, carried by 1 lb of rib, or 1 lb of rib and tie, for alternate design
The load supported per pound of member may be assumed proportional to the basic unit stress. Hence,
Use of the preceding equations will be illustrated by application to the Sherman Minton Bridge (Figs. 14.11 and 14.12). Its arches were fabricated mostly of A514 steel. Assume that a preliminary design has been made for the floor system and bracing. A preliminary estimate of weight of truss arch and tie is required.
From the data given for this structure in Art. 14.8, the total load per arch, excluding truss arch and tie, is