Chapter 4: Internal Loadings Developed in Structural Members Dr. Talal SALEM FE/DCEE

Chapter 4: Internal Loadings Developed in Structural Members CEN 210: Structures I 2 4-1 Internal Loadings at a Specified point The internal load at a specified point in a member can be determined by using the method of sections. For a coplanar structure this consists of: N, normal force V, shear force M, bending moment These loadings are the resultantsof the stress distributionover the cross-section.

Chapter 4: Internal Loadings Developed in Structural Members CEN 210: Structures I 3 4-1 Internal Loadings at a Specified point Sign Convention: Although the choice is arbitrary, the following convention has been widely accepted in structural engineering.

Chapter 4: Internal Loadings Developed in Structural Members CEN 210: Structures I 4 4-1 Internal Loadings at a Specified point Procedure for Analysis: Determine the support reactions. Keep all distributed loadings, couple moments & forces acting on the member in their exact location. Section the member ⊥to its axis at the point where the internal loading is to be determined. Draw a FBD of the segment that has the least no. of loads on it. Indicate the unknown resultants N, V& Macting in their positive directions. Solve the equations of equilibrium.

Chapter 4: Internal Loadings Developed in Structural Members CEN 210: Structures I 5 4-2 Shear and Moment Functions Design of beam requires detailed knowledge of the variationsof V& M. Internal Nis generally not considered as: The loads applied to a beam act perpendicular to the beam’s axis. For design purpose, a beam’s resistance to shear & bending is more important than its ability to resist normal force. An exception is when it is subjected to compressive axial force where buckling may occur.

Chapter 4: Internal Loadings Developed in Structural Members CEN 210: Structures I 6 4-2 Shear and Moment Functions In general, the internal shear & moment functions will be discontinuous or their slope will discontinuous at points where: The type or magnitude of the distributed load changes Concentrated forces or couple moments are applied.

Chapter 4: Internal Loadings Developed in Structural Members CEN 210: Structures I 7 4-3 Shear and Moment Diagrams for a Beam If the variations of V& Mare plotted, the graphs are termed the shear diagram and moment diagram. It can shown that: The slope of the shear diagram at a point is equal to the intensity of the distributed load at the point. The slope of the moment diagram is equal to the intensity of the shear at the point. ()xdVwdx= −dMVdx=

Chapter 4: Internal Loadings Developed in Structural Members CEN 210: Structures I 8 4-3 Shear and Moment Diagrams for a Beam These equations can be integrated: Change in Shear = Area under Distributed Loading Diagram.

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- Spring '17
- Force, Shear Stress, Truss, Shear Diagram