Linear Systems Analysis
The isolated suspension system is key part of the car. It is used to isolate the vibrations, improve road handling and ensure reliable cornering. In addition, the suspension system has to maintain the vehicle´s wheel geometry to maximize tyre contact with the road at all times, and react to the weight of the car during cornering to minimize body roll.
There are numerous types and configuration of suspension system that can be used in the cars. Usually the suspension system of front and back of the car is also different from each other. However, whilst suspension systems are a fundamental element of any vehicle and may appear to be relatively simple, designing and implementing them to balance passenger comfort with handling is a complex task.
The maximum vertical shear and end reactions for wheel loads on a simple span occur under the wheel over the support when the heaviest wheel (generally the rear wheel) is positioned at the support, with the remaining wheel loads on the span.
The absolute maximum vertical shear and end reaction for lane loads occur when the uniform load is continuous and the concentrated load for shear (PV) is positioned over the support.
Maximum end reactions computed by these procedures are based on the bridge span measured center to center of bearings and are commonly tabulated in bridge design specifications and handbooks. Although they are technically correct for point bearing at span ends only, they do provide a very close approximation of the actual reaction for short bearing lengths. For very long bearing lengths, reactions should be computed based on the out-to-out span length with loads placed at the span end.
Analysis:
For one lane of H 15-44 loading on a 62-foot simple span, we formulate the maximum moment, maximum reactions, and maximum vertical shear at a distance 10 feet from the supports.
Truck load consists of one 6,000-pound axle and one 24,000-pound axle with an axle spacing of 14 feet:
Maximum moment from truck loading will be computed first. The distance (x) of the load resultant from the 24,000-pound axle is determined
By summing moments about the 24,000-pound axle and dividing by the gross vehicle weight:
Maximum moment occurs under the 24,000-pound axle when the span centerline bisects the distance between the load resultant and the axle load
For lane loading, the concentrated load for moment is positioned at the span centerline:
439,890 ft-lb > 423,931 ft-lb, so lane loading produces maximum moment.
Maximum Reactions :
Truck loading, the maximum reaction is obtained by positioning the 24,000-pound axle over the support:
For lane loading, the maximum reaction is obtained by placing the concentrated load for shear over the support:
34,380 lb > 28,645 lb, so lane loading also produces the maximum reaction.
Maximum Vertical Shear:
10 feet from the Support For truck loading, the maximum vertical shear 10 feet from the support is obtained by positioning the 24,000-pound axle 10 feet from the support:
For lane loading, maximum vertical shear is obtained using a partial uniform load with the concentrated load for shear positioned 10 feet from the support:
26,822 lb > 23,806 lb and lane loading again controls maximum loading.
Matlab Approach AX=B :
Graphicals :
Max Vertical Shear :
