### 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 Example:

#### 46-2-01

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

### 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: