Short Answer:

Combined direct and bending stress is the condition when a structural member is subjected to both a direct load (tensile or compressive) and a bending moment at the same time. The direct load produces a uniform normal stress across the section, while the bending moment produces a varying stress — compressive on one side and tensile on the other.

When both these stresses act together, they combine to produce non-uniform stress distribution across the cross-section. This type of stress is commonly found in columns, beams, and other members subjected to axial loads acting with eccentricity, resulting in combined direct and bending stresses.

Detailed Explanation:

Combined Direct and Bending Stress

In engineering applications, a member is often subjected to multiple types of loads simultaneously. One of the most common cases is when a direct load and a bending moment act together on a structural or machine component. This condition gives rise to combined direct and bending stress.

A direct stress is caused by an axial load that acts along the centroidal axis of a member. It is uniform over the entire cross-section and can be either tensile stress (when the load pulls the member) or compressive stress (when the load pushes the member).

On the other hand, a bending stress is produced when a bending moment acts on the member. This stress is not uniform — one side of the member experiences tension and the opposite side experiences compression.

When both stresses act together, the result is a combined stress condition, in which the total stress at any point on the section is obtained by adding or subtracting the direct and bending stresses, depending on their direction.

Mathematical Expression

Consider a member of uniform cross-section subjected to:

1. A direct load (P) producing a direct stress (σd), and
2. A bending moment (M) producing a bending stress (σb).

Then,

and

Where,

•  = Axial load
•  = Cross-sectional area
•  = Bending moment
•  = Distance of the point from the neutral axis
•  = Moment of inertia of the section

The total stress at the extreme fibers is given by:

Therefore,

 

The positive sign (+) is used on the side where both stresses act in the same direction (increasing the total stress), and the negative sign (–) is used on the opposite side where they act in opposite directions (reducing the total stress).

Nature of Stress Distribution

1. If the load is purely axial:
   Only direct stress exists, and the stress is uniform across the section.
2. If only bending moment acts:
   Only bending stress is produced, which is zero at the neutral axis and maximum at the outermost fibers.
3. If both act together (combined direct and bending stress):
   The resulting stress is non-uniform, being maximum at one edge and minimum at the opposite edge. One side may experience higher compression or tension depending on the direction of the moment.

If the bending stress exceeds the direct stress, one edge may even come under tension, while the other remains in compression.

Practical Examples of Combined Direct and Bending Stress

1. Eccentrically Loaded Column:
   When a vertical column carries a load that does not pass through its centroid, the column experiences both a direct compressive load and a bending moment.
2. Beam with Axial Load:
   If a beam carries an axial load along with a transverse load, the combined effect produces both direct and bending stresses.
3. Crane Hook:
   The crane hook carrying a load experiences direct stress due to the pulling force and bending stress due to the curvature and eccentric loading.
4. Bracket or Frame:
   Structural brackets or machine frames often carry off-center loads, causing both direct and bending stresses.

Effects of Combined Direct and Bending Stress

1. Non-Uniform Stress Distribution:
   The stresses are not equally distributed across the section. One side of the member experiences greater stress, and the other side experiences lesser or opposite stress.
2. Possibility of Tensile Failure:
   When the bending stress is large enough, one side of the section may come under tension, which could lead to cracking in materials like concrete or cast iron that are weak in tension.
3. Reduced Strength:
   The combined stress condition reduces the safe load-carrying capacity of the member compared to a purely axial load case.
4. Deflection and Bending:
   The bending moment causes deformation, which affects the stability and alignment of structures.

Design Considerations

1. Strength Check:
   The maximum stress (compressive or tensile) produced by the combined action should not exceed the allowable stress of the material.
2. Avoiding Tension in Brittle Materials:
   For materials like concrete and cast iron, design is made such that the minimum stress (σmin) is always compressive to prevent cracks.
3. Ensuring Stability:
   Eccentricity should be minimized wherever possible to reduce bending moments and improve stability.
4. Factor of Safety:
   A sufficient factor of safety is applied to account for unknown stresses and imperfections in loading or material.

Practical Importance

The study of combined direct and bending stress is crucial because, in reality, very few structures or machine parts experience pure loading. Columns, beams, brackets, and machine frames often carry loads that cause both direct and bending effects.

By understanding this concept, engineers can calculate the resultant stresses accurately, design members that can withstand both effects, and prevent failures due to excessive stress or bending deformation.

Conclusion

Combined direct and bending stress occurs when a member is subjected to an axial load along with a bending moment. This causes both uniform direct stress and varying bending stress to act simultaneously, leading to non-uniform stress distribution. Such conditions are common in columns, beams, and other structural members subjected to eccentric loads. Proper analysis of combined stresses ensures safety, stability, and durability of mechanical and structural components under real working conditions.