Beam design is one of the most important tasks in structural engineering, where safety, stability, and cost-effectiveness depend on accurate analysis. To design any beam correctly, engineers rely on a combination of basic formulas and graphical tools such as shear force diagrams (SFD) and bending moment diagrams (BMD). These diagrams provide a clear visual understanding of how loads transfer through a structural member and how internal forces develop along its length.
A beam carries loads through bending, and this bending action is governed by three key relationships: load, shear, and moment. The load placed on a beam creates shear forces, and these shear forces generate bending moments. By understanding these relationships, engineers can determine the critical sections where maximum stresses occur. For example, in a simply supported beam with a point load at midspan, the maximum shear occurs near the supports, while the maximum bending moment appears at the center. These insights help in selecting the correct beam size and reinforcing the right locations.
Shear force diagrams are essential because they show the variation of shear along the beam. Sudden jumps in the SFD indicate point loads, while linear changes represent uniform loads. Similarly, bending moment diagrams illustrate how bending stresses accumulate. A triangular or parabolic BMD often indicates distributed loads, while straight-line segments show simpler loading conditions. Interpreting these diagrams correctly ensures that the beam’s cross-section can resist forces without exceeding allowable stress limits.
The moment of inertia (I) and modulus of elasticity (E) further determine how much a beam will bend or deflect under load. Many design codes require deflection checks in addition to strength checks to ensure comfort and durability.
In practice, engineers often use standard formulas for common beam setups—simply supported, cantilever, continuous, and fixed beams—along with SFD and BMD to verify the safety of structural members. Mastering these concepts leads to stronger, more efficient, and more reliable designs.
Beam Design Formulas with Shear and Moment Diagrams
• Simple Beam – Uniformly Distributed Load
• Simple Beam – Uniform Load Partially Distributed
• Simple Beam – Uniform Load Partially Distributed at One End
• Simple Beam – Uniform Load Partially Distributed at Each End
• Simple Beam – Load Increasing Uniformly to One End
• Simple Beam – Load Increasing Uniformly to Center
• Simple Beam – Concentrated Load at Center
• Simple Beam – Concentrated Load at Any Point
• Simple Beam – Two Equal Concentrated Loads Symmetrically Placed
• Simple Beam – Two Equal Concentrated Loads Unsymmetrically Placed
• Simple Beam – Two Unequal Concentrated Loads Unsymmetrically Placed
• Simple Beam – Uniformly Distributed Load
• Cantilever Beam – Concentrated Load at Free End
• Cantilever Beam – Concentrated Load at Any Point
• Beam Fixed at One End, Supported at Other – Uniformly Distributed Load
• Beam Fixed at One End, Supported at Other – Concentrated Load at Center
• Beam Fixed at One End, Supported at Other – Concentrated Load at Any Point
• Beam Fixed Among One Support – Uniformly Distributed Load
• Beam Overhanging One Support – Uniformly Distributed Load on Overhang
• Beam Overhanging One Support – Concentrated Load at End of Overhang
• Beam Overhanging One Support – Concentrated Load at Any Point Between Supports
• Beam Overhanging Both Supports – Unequal Overhangs – Uniformly Distributed Load
• Beam Fixed at Both Ends – Uniformly Distributed Load
• Beam Fixed at Both Ends – Concentrated Load at Center
• Beam Fixed at Both Ends – Concentrated Load at Any Point
• Continuous Beam – Two Equal Spans – Uniform Load on One Span
• Continuous Beam – Two Equal Spans – Concentrated Load at Center of One Span
• Continuous Beam – Two Equal Spans – Concentrated Load at Any Point
• Continuous Beam – Two Equal Spans – Uniformly Distributed Load
• Continuous Beam – Two Unequal Spans – Two Equal Concentrated Loads Symmetrically Placed
• Continuous Beam – Two Unequal Spans – Concentrated Load on Each Span Symmetrically Placed
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