Strut-and-tie modeling - Computational Analysis and Design of Bridge Structures - page 421

2 L /5, 3 L /5, and 4 L /5 from the end support, and other wheels follow the
location of the wheel spacing. As shown in Figure 13.13b, crane loads are
applied at the top of the deep beam, and the self-weight of the deep beam
is considered as loads to the deck. The crane load consists of eight wheels,
each 180.5 kip (802.90 kN) (factored). The envelope results for each case
are tabulated in the study report to the Maryland Port Authority (Fu
1994).
Results from the CAST for all the five configurations are shown in
Figure 13.13c. For Case No. 4B, the maximum tension force is 61.45 kip
(273.34 kN) and the maximum compression force is 201.84 kip (897.83 kN).
Beam thickness is 609.6 mm (24″). Based on wheel contact width and height
of rail, the width of the strut will be 254 mm (10″) minimum; hence the
strut section considered is 254 mm × 609.6 mm (10″ × 24″). Reinforcements
of four no. 6 rebars are provided at the top and bottom for the tie members.
Truss forces and stress interaction (actual/allowable) ratios are well below
unity for all the members.
After achieving the solution for the members, a detailed nodal analysis is
performed. With 254-mm (10″) width struts, the nodes at the bottom ends
of the most heavily loaded members were overstressed. A few iterations
were necessary to optimize the strut width (ranging from 254 mm [10″]
to 304.8 mm [12″]) so that the stress triangles within the nodal zone get
reoriented and meet the strength requirement of the code-specified limit of
the nodal zone.
The stress fields in struts and ties are idealized to be uniaxial, whereas
the stress fields in nodal zones are biaxial. These conditions cause stress
discontinuity at the interface of the strut and node stress fields and at the
interface of the tie and node stress fields. The stress discontinuity also
occurs along the longitudinal boundary of the strut or tie stress fields if the
selected stress distribution across the effective width is uniformly distrib-
uted. For 2D structures, the interface between two different stress fields is
commonly referred to as the line of stress discontinuity. Although the term
line is used, the stress discontinuity actually occurs on a surface perpendic-
ular to the plane of the structures, across the D-region thickness. For this
reason, reinforcement is required at the nodal locations perpendicular to
the plane of the structures. This reinforcement can be seen in Figure 13.11b
provided for the case 1 example.
13.6 2d/3d illuStrated exaMPle 4—HaMMerHead
Pier of tHoMaS JefferSon BridGe
This structure is located in St. Mary's and Calvert counties in Southern
Maryland (Fu et al. 2005). It was completed and put into service in 1977.
During an inspection in 1979, cracks were observed in the deepwater