
MECHANICS  CASE STUDY



Introduction

A truck moving across a
simplysupported bridge 

After watching a truck driving across a bridge, Daniel, a new engineering student, wonders if it is possible to determine the worst bending moment. He knows how to find the bending moment when the load location is given, but not when it can be at any location. 



Load Distribution on Wheels


What is known:
 Bridge is assumed to b simplysupported
 Bridge length is 50 m
 Wheel locations are 5 m, 10 m, and 12 m from the front wheel as shown in the diagram
 Total truck weight is 140 kN
 Truck weight is unevenly distributed to the wheels; front wheels, F_{1}, carries 15%, second set of wheels, F_{2}, carries 25%, and remaining weight is equally carried on the back two wheel sets, F_{3} and F_{4}.






Question



What is the maximum bending moment that occurs when the truck moves across the bridge? Note, the location of the truck that causes the maximum moment is not given and needs to be determined. 





Approach



 Determine the weight on each wheel.
 Find the position of total resultant force, 140 kN, with respect to one of the wheels.
 Find the position of the truck where maximum bending moment will occur.
 Using static equilibrium equations
Σ F = 0 and Σ M = 0
calculate reaction forces occurred at the support for a particular position of the truck.
 Again use the static equilibrium equations to calculate the bending moment at various sections in the beam.
 Then calculate the bending moments by taking forces at various positions.

