A structural engineer must determine which type of steel to select for a beam, but the weight limitation cannot exceed 7 tons. The project has narrowed the choices down to A36 steel (ρ = 7800 kg/m³) and A992 steel (ρ = 7850 kg/m³). However, the engineer needs to determine the load difference between an A36 and A992 steel box beam with an inertia of 249 in⁴, and has an elastic modulus of 30 x 10⁶ PSI & 35 x 10⁶ PSI, respectively.
The A36 steel is designed to deflect 0.11" while the A992 steel is designed to deflect 0.18". Both beams have a span length of 6.1 meters, a distributed stress of 67 kN/m², full length of 7.8 m, and the beam is in a simple load configuration. Determine the load difference between the two beam options at the design limit.
What is your calculated answer most closely to?
1.5 tons
2.5 tons
3.5 tons
4.5 tons