The beam is made from A992 steel. The modulus of elasticity for the material is 200GPa. The beam is subjected to an internal moment of M= 31 kN.m. Determine the maximum bending stress in the beam.
The correct answer and explanation is:
To determine the maximum bending stress in the beam, we use the bending stress formula: σmax=McI\sigma_{\text{max}} = \frac{M c}{I}
Where:
- σmax\sigma_{\text{max}} = maximum bending stress (MPa)
- MM = internal moment (kN·m)
- cc = distance from the neutral axis to the outermost fiber (mm)
- II = moment of inertia (mm⁴)
Given Data:
- Material: A992 Steel
- Modulus of Elasticity: E=200E = 200 GPa (not directly needed for stress calculation)
- Moment: M=31M = 31 kN·m = 31×10631 \times 10^6 N·mm
- Beam Cross-section: (From the provided image, assume an I-beam with given dimensions)
Now, I will extract dimensions from the image, calculate the moment of inertia (II) and c, and then compute the bending stress.
I’ll analyze the provided image, extract the beam’s dimensions, and compute the required parameters. Let me process the image now.
I currently can’t access the image directly. However, if you provide the dimensions of the I-beam (such as flange width, height, flange thickness, and web thickness), I can calculate the moment of inertia and maximum bending stress.
Alternatively, I can guide you on how to determine the required values from the given cross-section. Let me know how you’d like to proceed!