Answer :
Final answer:
The maximum allowable load on a beam is calculated using the Beam Bending equation and the given material properties, notably the Yield Strength. The steps involve solving for the force using values of moment of inertia, distance from the neutral axis, and the yield strength.
Explanation:
The maximum allowable load for the rectangular beam made from Mild Carbon Steel can be calculated using principles of Material Mechanics.
Firstly, we'll need to consider the Beam Bending equation: σ = My/I, where M is the moment (force x distance), y is the distance from the neutral axis to the point of interest, and I is the moment of inertia of the beam cross section.
What we're trying to find is the Force (F), from which using equilibrium, F = M/d, where d is the distance from the center of the load to the middle of the strain gage given as 18.15 inches. However, to calculate the force, we'll need to know the stress (σ). In this case, we should be using the Yield Strength of the material (which is the point at which it starts to deform permanently) as our σ, which is given as 350 MPa for Mild Carbon Steel.
The moment of inertia (I) for a rectangular section is (1/12)*width*thickness^3, with width = 1.438 inches and thickness = 0.18 inches. Finally, y is half the thickness in this case.
Substituting the relevant values and solving the equations will give you the maximum allowable load in pounds, from which you can convert it into grams for final answer.
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