BEAM FORMULAS WITH SHEAR AND MOMENT DIAGRAMS by American Wood Council
The American Wood Council (AWC) is part of the wood products group of the American Forest & Paper Association (AF&PA). AF&PA is the national trade association of the forest, paper, and wood products industry, representing member companies engaged in growing, harvesting, and processing wood and wood fiber, manufacturing pulp, paper, and paperboard products from both virgin and recycled fiber, and producing engineered and traditional wood products. For more information see www.afandpa.org.
Figures 1 through 32 provide a series of shear and moment diagrams with accompanying formulas for design of beams under various static loading conditions. Shear and moment diagrams and formulas are excerpted from the Western Woods Use Book, 4th edition, and are provided herein as a courtesy of Western Wood Products Association.
List of Figures
Figure 1 Simple Beam – Uniformly Distributed Load
Figure 2 Simple Beam – Uniform Load Partially Distributed
Figure 3 Simple Beam – Uniform Load Partially Distributed at One End
Figure 4 Simple Beam – Uniform Load Partially Distributed at Each End
Figure 5 Simple Beam – Load Increasing Uniformly to One End
Figure 6 Simple Beam – Load Increasing Uniformly to Center
Figure 7 Simple Beam – Concentrated Load at Center
Figure 8 Simple Beam – Concentrated Load at Any Point
Figure 9 Simple Beam – Two Equal Concentrated Loads Symmetrically Placed
Figure 10 Simple Beam – Two Equal Concentrated Loads Unsymmetrically Placed
Figure 11 Simple Beam – Two Unequal Concentrated Loads Unsymmetrically Placed
Figure 12 Cantilever Beam – Uniformly Distributed Load
Figure 13 Cantilever Beam – Concentrated Load at Free End
Figure 14 Cantilever Beam – Concentrated Load at Any Point
Figure 15 Beam Fixed at One End, Supported at Other – Uniformly Distributed Load
Figure 16 Beam Fixed at One End, Supported at Other – Concentrated Load at Center
Figure 17 Beam Fixed at One End, Supported at Other – Concentrated Load at Any Point
Figure 18 Beam Overhanging One Support – Uniformly Distributed Load
Figure 19 Beam Overhanging One Support – Uniformly Distributed Load on Overhang
Figure 20 Beam Overhanging One Support – Concentrated Load at End of Overhang
Figure 21 Beam Overhanging One Support – Concentrated Load at Any Point Between Supports
Figure 22 Beam Overhanging Both Supports – Unequal Overhangs – Uniformly Distributed Load
Figure 23 Beam Fixed at Both Ends – Uniformly Distributed Load
Figure 24 Beam Fixed at Both Ends – Concentrated Load at Center
Figure 25 Beam Fixed at Both Ends – Concentrated Load at Any Point
Figure 26 Continuous Beam – Two Equal Spans – Uniform Load on One Span
Figure 27 Continuous Beam – Two Equal Spans – Concentrated Load at Center of One Span
Figure 28 Continuous Beam – Two Equal Spans – Concentrated Load at Any Point
Figure 29 Continuous Beam – Two Equal Spans – Uniformly Distributed Load
Figure 30 Continuous Beam – Two Equal Spans – Two Equal Concentrated Loads Symmetrically Placed
Figure 31 Continuous Beam – Two Unequal Spans – Uniformly Distributed Load
Figure 32 Continuous Beam – Two Unequal Spans – Concentrated Load on Each Span Symmetrically Placed