A beam has a hollow rectangular cross section with external dimensions of 80 mm wide and 120 mm deep, and internal dimensions of 50 mm wide and 90 mm deep. The maximum tensile stress of the beam must not exceed 350 MPa. Calculate the maximum allowable bending moment.

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

Learn more about calculating the maximum allowable bending moment of a beam with a hollow rectangular cross section here:

https://brainly.com/question/33794651

#SPJ11