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### Curved Rectangular Tube Section Stress Calculations

Beam Deflection and Stress Calculators with Formulas

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

Preview Curved Square / Rectangular Tube Section Beam Stress Calculator

Figure 2.0 Square / Rectangular Tube Section Beam Dimensions

Stress Distribution due to bending is given by:

*Equation 1
s = M · γ / ( A · e · ( r _{n} - 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, in^{2}

e = distance from the center of gravity axis to the neutral axis, inches

*r _{n}* = 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 · h _{i} ) / ( A · e · r_{i} ) *

Where:

*h _{i}* = distance from the center neutral axis to the inside fiber, inches (

*h*)

_{i}= r_{n}- r_{i}*r*= radius of curvature on the inside fiber, inches

_{i}Bending Stress at the Outside Fiber is given by:

*Equation 3
s = ( M · h _{o} ) / ( A · e · r_{i} ) *

Where:

*h _{o}* = distance from the center neutral axis to the inside fiber, inches (

*h*)

_{o }= r_{o}- r_{i}*r*= radius of curvature on the outside fiber, inches

_{o}*A = ( b - t ) ( t*

_{i}+ t_{o}) + thTrapezoid Section Beam Stuctural Shape

*r _{n} = [ *

*( b - t ) ( t*

_{i}+ t_{o}) + th ] /*[ b [ log*

^{e}( ( r_{i}+ t_{i}) / r_{i}) + log_{e}( r_{o}/ ( r_{o}- t_{o}) ) ] + t log_{e}( ( r_{o}- t_{o}) / ( r_{i}+ t_{i}) ]*e* = R - *r _{n}*

*R = r _{i} + [ ( 1/2) h^{2} t + (1/2) t_{i} ( b-t ) + ( b-t ) ( t_{o} ) ( h - (1/2) t_{o } ]
/
( ht + ( b-t) (t_{i} + t_{o}) ) *

Where:

*b* = Tube Section beam width, in

*h* = width, in

*t _{i}* = wall thickness, in

*t*= wall thickness, in

_{o}Related:

- Curved Trapezoid Section Woth Moment Load Applied Stress Calculations
- Curved T-Section Stress Formulas and Calculator
- Curved I-Beam Section Stress Formulas and Calculator
- Curved Circular Beam Stress Formulas and Calculator
- Curved Rectangular Beam Stress Formulas and Calculator
- Curved Beam Stress Deflection Design Spreadsheet Calculator
- Strength of Materials Basics and Equations | Mechanics of Materials
- Civil Engineering Design Knowledge
- Double Integration Method for Beam Deflections
- Double Integration Method Example 5 Proof Pinned Supported Beam
- Bending, Deflection and Stress Equations Calculator for Beam Fixed at One End, Supported at the Other, Load at Center

References:

- McGraw Hill Machine Design (1968)