"Shared hosting space may only be used for web files, active email and content of User Websites. Shared hosting space may not be used for storage (whether of media, emails, or other data), including, as offsite storage of electronic files, email or FTP hosts. HostGator expressly reserves the right to review every shared account for excessive usage of CPU, disk space and other resources that may be caused by a violation of this Agreement or the Acceptable Use Policy. HostGator may, in our sole discretion, terminate access to the Services, apply additional fees, or remove or delete User Content for those accounts that are found to be in violation of HostGator's terms and conditions."
A site with 70 to 80 concurrent visitors is way outside the scope of what I would normally consider shared hosting to be valid for.
The only clients I recommend shared hosting for have static "business card" websites that receive a few dozen hits a month and who are OK with downtime.
There are exceptions to this such as Rackspace Cloud Sites but I am assuming we are talking about "cheap" shared hosting.