Question 8.4: Compute the shearing stress at the axis a–a for a beam with ...
Compute the shearing stress at the axis a–a for a beam with the rectangular cross section shown in Figure 8–7. The shearing force, V, on the section of interest is 5400 N.
Objective Compute the shearing stress at the axis a–a.
Given Cross-section shape and dimensions in Figure 8–7. V = 5400 N.
Analysis Use the Guidelines for Computing Shearing Stresses in Beams.
Results Step 1. V = 5400 N (given).
Step 2. For the rectangular shape, the centroid is at the midheight, as shown in Figure 8–7, coincident with axis a–a. \bar{Y} =125 0.mm
Step 3. I = bh^{3} /12 = (50) (250)³/12 = 6.51 × 10^{7} mm^{4}.
Step 4. Thickness = t = 50 mm at axis a–a.
Step 5. Normally we would compute Q = A_{p} \bar{y} =using the method shown earlier in this chapter.
But the value of Q for the section in Figure 8–7 was computed in Example Problem 8–1. Use Q = 390 625 mm³.
Step 6. Using Equation (8–1),
\tau = \frac{VQ}{It} = \frac{(5400 N)(390 625 mm^{3})}{(6.51 \times 10^{7} mm^{4})(50 mm)} = 0.648 N/mm² = 648 kPa
Comment The shearing stress at the midheight of the rectangular section in Figure 8–7 is 648 kPa.
It will be shown later that this is the maximum shearing stress on the section.