Material Subjected to Combined Axial & Bending Stresses

  • Identify members in combined Axial and Bending stresses.

  • Find maximum and minimum stresses in member undergoing combined stresses.

  • Plot total stress variation diagram for the members under combined stresses.

It is applicable for an eccentrically loaded column. A beam carries transverse loads (bending loads) and a column carries an axial compressive load. Examples of beam column are chimneys, dams, retaining wall, trees, poles, building and structures. Axial compressive load is due to the self-weight and the bending is due to the wind effect. Under these situations, the beam will have following stresses.

  • Axial stresses are compressive stresses of constant value, \(\sigma_A = \dfrac{P}{A}\)

  • Bending stresses are both simultaneously tensile and compressive stresses and are of varying values. These bending stresses will be maximum at the outermost fibres i.e. at \(y_{max}\). \[\sigma_b = \left(\dfrac{M}{I}\right) y_{max}\]

So, maximum compressive stress \(\sigma_{max} = \sigma_A + \sigma_b\) Maximum tensile stress \(\sigma_x\) = \(\sigma_b\)\(\sigma_A\) i.e. tensile stress will be there only if \(\sigma_b > \sigma_A\).

Solved Examples

Solved Example:

46-2-01

Which of the following is NOT an assumption while deriving the formula for bending stress?

Correct Answer: B

Solved Example:

46-2-02

The bending moment M and a torque T is applied on a solid circular shaft. If the maximum bending stress equals to maximum shear stress developed, then M is equal to:

Correct Answer: A

Solved Example:

46-2-03

A 20 mm diameter circular rod carries a pull parallel to the centroidal axis at a distance from it. Find the eccentricity if the maximum stress is 20 percent greater than the mean stress at a section normal to the axis. (JKSSB JE CE Oct 2021- Shift II)

Correct Answer: C