Question 4.CS.1: The Mianus River Bridge in Greenwich, Connecticut, is a 24-s...
The Mianus River Bridge in Greenwich, Connecticut, is a 24-span highway structure completed in 1958 that carries Interstate 95 over the Mianus River. Using separate northbound and southbound roadways, each direction includes two 100-ft-long skewed suspended spans that are supported by cantilevered girders at either end (CS Fig. 4.1). The suspended spans themselves contain two girders, with each attached to the cantilevered support girders using pillow-block bearings (which function as pin supports) at one end and twin hangers at the other end. CS Fig. 4.2 depicts the hanger connection, which functions as a link support. On June 28, 1983, one of the northbound suspended spans collapsed, with two automobiles and two trucks plunging into the void (CS Photo 4.1), killing three people and seriously injuring three more. The cause was determined to be corrosion-induced lateral displacement of the lower pin cap that secured the hangers onto the pin supporting the south girder, causing one of the hangers to work itself off the pin and transferring all load at this corner to the remaining hanger. The resulting increase in loading on the two pins eventually caused the upper pin to fracture, leading to the collapse of the entire span. The corrosion was accelerated by water and deicing agents draining through the deck expansion joint and regularly wetting the hanger connection. Compounding the situation was an inadequate routine inspection program that resulted in the severely compromised hanger condition remaining undetected before failing.*
Among the loads that the bridge was designed to support is a live load consisting of a standard truck, as shown in CS Fig. 4.3, placed in each of the three lanes of travel. Considering this live load (and disregarding any effects of the skewed deck), let’s determine the maximum value of the resulting support reaction at the failed hanger connection.
STRATEGY: Disregarding the effects of the skewed deck and positioning the three trucks so that they are aligned with each other as they travel over the three lanes, we will assume that the live load is equally distributed to the two girders. The live load carried by the south suspended girder will then be equivalent to the axle loads of 1.5 trucks, as shown in CS Fig. 4.4. It can be demonstrated that the maximum hanger reaction (at support B) will occur when one of the axle loads is positioned at this end of the girder. Considering the three possible cases, this reaction can then be determined by drawing the free-body diagram of the south girder and summing moments about end A.
*Ref: “Highway Accident Report–Collapse of a Suspended Span of Interstate Route 95 Highway Bridge Over the Mianus River, Greenwich, Connecticut, June 28, 1983,” Report No. NTSB/HAR-84/03, National Transportation Safety Board, July 19, 1984.
MODELING: The free-body diagram for Case I is shown in CS Fig. 4.5, where the 12-kip axle is positioned at the end of the girder. Note that there is a short offset between this point and the hanger at B. Relative to the 100-ft span, the length of this offset is very small, and will therefore be disregarded for the purposes of this analysis. In the same manner, the free-body diagram for Case II is shown in CS Fig. 4.6, where the middle axle is now positioned at the end of the girder. Case III (not shown) would have the last axle placed at the end of the girder.
ANALYSIS:
Case I: Lead Axle at End of Girder. Referring to the free-body diagram of CS Fig. 4.5, set the sum of the moments of all external forces about point A equal to zero:
+\circlearrowleft \Sigma M_A = 0: +B(100 ft)−(48 kips)(72 ft)− (48 kips)(86 ft)−(12 kips)(100 ft)= 0
B = 87.8 kips B = 87.8 kips ↑
Case II: Middle Axle at End of Girder. As shown in CS Fig. 4.6, the lead axle no longer acts on the suspended girder, and should therefore not be included in its equilibrium analysis. (It would thus be appropriate to not show this force at all with the girder’s free-body diagram.) Setting the sum of the moments about point A equal to zero of only those external forces acting on the girder:
+\circlearrowleft \Sigma M_A=0: \quad +B(100 ft)−(48 kips)(86 ft)−(48 kips)(100 ft)= 0
B = 89.3 kips B = 89.3 kips ↑
Case III: Last Axle at End of Girder. Here, the only axle remaining on the girder is the trailing 48-kip axle. With it positioned at the end of the girder, by inspection it is apparent that the reaction at B is equal to this force.
B = 48 kips ↑
Comparing the three cases, we conclude that Case II governs.
\pmb{B}_{\max} = 89.3 kips ↑
REFLECT and THINK: In addition to the live load considered here, this hanger is subject to other loads as well. Among these are the dead load (i.e., self-weight of the suspended span) and an impact load that is a code-prescribed percentage of the live load. Also note that if it were possible for the truck to be reversed and travel backward, we would obtain an even larger maximum live-load hanger reaction (97.9 kips) when the now-leading 48-kip axle is positioned at the hanger end of the girder, and with the other two axles trailing behind.
