Answer :
The maximum bending stress in the simply supported beam is [tex]5.29 * 10^7 Pa.[/tex]
We can substitute the values of M, c, and I into the bending stress formula to find the maximum bending stress in the beam.
The maximum bending stress in a simply supported beam can be determined using the formula:
σ = (M * c) / I
Where:
σ is the bending stress
M is the bending moment
c is the distance from the neutral axis to the extreme fiber (half the depth of the beam)
I is the moment of inertia of the beam section
First, we need to calculate the bending moment at the midpoint of the beam. Since the mass is located at the midpoint, the bending moment can be calculated as:
M = (weight * distance) / 2
Given that the weight is 2700 kg and the distance is 0.5 m (half the length of the beam), we can substitute these values into the formula:
[tex]M = (2700 kg * 9.81 m/s^2 * 0.5 m) / 2[/tex]
M = 6613.5 Nm
Next, we need to calculate the moment of inertia of the beam section. For a rectangular beam, the moment of inertia can be calculated as:
[tex]I = (b * d^3) / 12[/tex]
Given that the width (b) is 75 mm and the depth (d) is 100 mm, we need to convert these dimensions to meters:
b = 75 mm = 0.075 m
d = 100 mm = 0.1 m
Substituting these values into the formula, we can calculate the moment of inertia:
[tex]I = (0.075 m * 0.1 m^3) / 12[/tex]
[tex]I = 6.25 * 10^-5 m^4[/tex]
Finally, we can substitute the values of M, c, and I into the bending stress formula to find the maximum bending stress in the beam:
[tex]σ = (6613.5 Nm * 0.05 m) / 6.25 * 10^-5 m^4[/tex]
[tex]σ = 5.29 * 10^7 Pa[/tex]
Therefore, the maximum bending stress in the beam is [tex]5.29 * 10^7 Pa.[/tex]
Note: Pa stands for Pascals, which is the unit of pressure or stress.
In conclusion, the maximum bending stress in the simply supported beam is [tex]5.29 * 10^7 Pa.[/tex]
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