Our client is a chemical company that wants to expand its operations across a street and rail line. The expansion requires connecting the two facilities by several pipes. The site is just below an...

Our client is a chemical company that wants to expand its operations across a street and rail line. The expansion requires connecting the two facilities by several pipes. The site is just below an elevated highway, so the company cannot run the pipes underground. Working with the client, our principal-in-charge has decided to use an arch to carry the pipes over the road and rail line. Because of the tight geometry of the site and the close proximity to the road and rail line, the senior engineer has chosen to use a semi-circular arch even though that is not the ideal shape for the loads. Another team member will be performing computer-aided analysis of the arch. Our task is to generate approximate results that we can use to validate the computer results. The primary load will be the self-weight of the truss and pipes, so we will analyze the arch subjected to dead load. Because the load is distributed along the length, it is not uniform along the horizontal axis. For this comparison we want approximate reactions, therefore we can consider the resultant of the distributed load on each half of the arch. A team member has calculated the forces and their locations.

a. Guess whether the reactions will have a larger vertical or horizontal magnitude.

b. Approximate the arch as a three-hinge arch. Find the vertical and horizontal reactions.

c. Comment on why your guess in part (a) was or was not the same as what you discovered in part (b).