Answer :
Final answer:
The maximum allowable bending moment of the beam is 8,064,000 Nmm.
Explanation:
To calculate the maximum allowable bending moment of the beam, we need to calculate the section modulus of the hollow rectangular cross section and then use it in the formula: Maximum Allowable Bending Moment = (Maximum Tensile Stress) * (Section Modulus).
First, let's calculate the moment of inertia of the hollow rectangular cross section:
Moment of Inertia = (Width * Height^3 - Internal Width * Internal Height^3) / 12
Substituting the given values:
Moment of Inertia = (80 * 120^3 - 50 * 90^3) / 12
Moment of Inertia = 1,382,400 mm^4
Next, let's calculate the section modulus:
Section Modulus = (Moment of Inertia) / (Distance from Neutral Axis)
Since the beam is symmetric, the distance from the neutral axis is half of the depth:
Distance from Neutral Axis = 120 / 2 = 60 mm
Substituting the values:
Section Modulus = 1,382,400 / 60 = 23,040 mm^3
Finally, let's calculate the maximum allowable bending moment:
Maximum Allowable Bending Moment = (Maximum Tensile Stress) * (Section Modulus)
Substituting the given value:
Maximum Allowable Bending Moment = 350 * 23,040 = 8,064,000 Nmm
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