Question 7.3: Figure 7–15 shows the bending moment diagram for a 8.0 m lon...
Figure 7–15 shows the bending moment diagram for a 8.0 m long beam in a large machine structure. It has been proposed that the beam be made from a standard IPE 360×170 steel shape. Compute the maximum stress due to bending in the beam.
Objective Compute the maximum stress due to bending.
Given Bending moment diagram shown in Figure 7–15; IPE 360×170 beam shape
Analysis Use Equation (7–1). In Figure 7–15, identify the maximum bending moment on the beam to be 128 533 N · m at point F. Find the values of I and c from the table of properties for IPE shapes in Appendix A–7(e).
Results The moment of inertia with respect to the x-axis is I_{x} = 1.627 × 10^{8} mm^{4} .
To determine the value of c, we need to find first the depth of the IPE shape. Note that the depth is the vertical height, given to be d = 360 mm. Then,
c = d/2 = 360 mm/2 = 180 mm
\sigma_{max} = \frac{Mc}{I} = 128 533 N·m \left\lgroup \frac{1000 mm}{1.627 × 10^{8} mm^{4}}\right\rgroup = 142.2 MPa
Comment This maximum stress would occur as a tensile stress on the bottom surface of the beam and as a compressive stress on the top surface at the position F. Because this is a relatively long beam, it must be laterally braced as described in Reference 2.