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### Curved Rectangular Tube Section Stress Calculations

Curved Square / Rectangular Tube Section Stress Formulas and Calculator With Moment Loading Applied

Figure 1.0

Figure 2.0 Square / Rectangular Tube Section Beam Dimensions

Stress Distribution due to bending is given by:

Equation 1
s = M · γ / ( A · e · ( rn - y ) )

Where:

s = the bending stress, psi
M = bending moment with respect to the centroical axis, in-lb
y = distance from the neutral axis to the point in question, inches (positive for distances toward the center of curvature, negative for distances away from the center of curvature)
A = the area of the section, in2
e = distance from the center of gravity axis to the neutral axis, inches
rn = radius of curvature of the neutral axis, inches
value of e used for base log = 2.7182818

Bending Stress at the Inside Fiber is given by:

Equation 2
s = ( M · hi ) / ( A · e · ri )

Where:

hi = distance from the center neutral axis to the inside fiber, inches ( hi = rn - ri )
ri = radius of curvature on the inside fiber, inches

Bending Stress at the Outside Fiber is given by:

Equation 3
s = ( M · ho ) / ( A · e · ri )

Where:

ho = distance from the center neutral axis to the inside fiber, inches ( ho = ro - ri )
ro = radius of curvature on the outside fiber, inches
A = ( b - t ) ( ti + to ) + th

Trapezoid Section Beam Stuctural Shape

rn = [ ( b - t ) ( ti + to ) + th ] / [ b [ loge ( ( ri + ti ) / ri ) + loge ( ro / ( ro - to) ) ] + t loge ( ( ro - to ) / ( ri + ti ) ]

e = R - rn

R = ri + [ ( 1/2) h2 t + (1/2) ti ( b-t ) + ( b-t ) ( to ) ( h - (1/2) to ] / ( ht + ( b-t) (ti + to) )

Where:

b = Tube Section beam width, in
h = width, in
ti = wall thickness, in
to = wall thickness, in

Related:

References:

• McGraw Hill Machine Design (1968)