Calculating the BIGGEST BENDING TENSION - PROBLEM 6.59 | Mechanics of Materials

PROBLEM 6.59
Determine the greatest bending stress developed in the element if it is subjected to an internal bending moment M = 40 kN.m.
00:00 Calculation of the Centroid of the Cross Section
✅ The first step to be done is to divide the cross section into three flat figures (2 rectangles and 1 circle) and identify the location of the centroid of each figure in relation to the base of the cross section.
Once the centroids of each figure have been located, now just replace the cross section centroid in the formula, given by:
ycg = ΣA'.y'cg/ΣA, where:
y'cg = centroid of each figure
A' = area of ​​each figure
03:10 Calculation of the Moment of Inertia of the Cross Section
✅ To calculate this other geometric property, we have to divide the cross-sectional area into 3 rectangles, and then apply the following formula:
I = Σ(I' + A.d²), where:
I' = moment of inertia of each figure in relation to its centroid
A = area of ​​each figure
d = distance between the centroid of the cross section and the centroid of each figure
If so far you still have difficulties in calculating the centroid and the moment of inertia of the cross section, then I suggest you watch this video 👇:
• Como Calcular o CENTRO...
06:20 Calculation of the Maximum Bending Stress
✅ Very well, now we have all the necessary data to calculate the maximum bending stress developed in the element, which is calculated using the following formula:
σmax = M.c/I, where:
c = perpendicular distance from the neutral axis to a point farther from the neutral axis
M = internal bending moment applied around the neutral axis (it was given in the problem)
📚 Source: Mechanics of Materials 7th Ed. (R.C. Hibbeler)
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LIKE!!!!!!!! Usa qual programa para escrever as formulas????

Valeu, uso PowerPoint.