Bending Stress

Question 1

maximum stress in a curved beam

Answer 1

σ max = Mh / AeR

*bending moment (M)
*distance from the neutral axis to the innermost side (h)
*cross-sectional area (A)
*distance from the centroid of the cross-section to the neutral axis (e)
*radius of curvature of the neutral axis (R)

Question 2

minimum stress in a curved beam

Answer 2

σ max = -Mh / AeR

*bending moment (M)
*distance from the neutral axis to the outermost side (h)
*cross-sectional area (A)
*distance from the centroid of the cross-section to the neutral axis (e)
*radius of curvature of the neutral axis (R)

Question 3

distance to neutral axis from axis of rotation

Answer 3

r = A / ∫ da/ λ

cross-sectional area (A)
distance from neutral axis (λ)
da = b dλ

Question 4

stress in a curved beam

Answer 4

σ = My / Ae(r - y)

*bending moment (M)
*distance from neutral axis (y)
*cross-sectional area (A)
*distance from the centroid of the cross-section to the neutral axis (e)
*distance to neutral axis from axis of rotation

Question 5

r for a rectangular curved bean

Answer 5

r = h / ln(R2/R1)

*height of beam (h)
*distance to lower edge from axis of rotation (R1)
*distance to upper edge from axis of rotation (R2)

Question 6

radius of neutral axis, on a loaded and unloaded curved beam

Answer 6

unloaded:
rφ

loaded:
(r + δr)(φ - δφ)

radius(r)
angle(φ)

Question 7

how do you find the centroid of an area

Answer 7

x = ∑(A⋅x) / ∑A
y = ∑(A⋅y) / ∑A