Structure Analysis I

Lecture 7 Internal Loading Developed in Structural Members Ch.4 in text book

Internal loading at a specified Point In General The loading for coplanar structure will consist of a normal force N, shear force V, and bending moment M. These loading actually represent the resultants of the stress distribution acting over the member’s cross-sectional are

Sign Convention +ve Sign

Procedure for analysis Support Reaction Free-Body Diagram Equation of Equilibrium

Example 1 Determine the internal shear and moment acting in the cantilever beam shown in figure at sections passing through points C & D

Example 2 6kN Determine the internal shear and moment acting in section 1 in the beam as shown in figure 18kN

Example 3 Determine the internal shear and moment acting in the cantilever beam shown in figure at sections passing through points C

Shear and Moment function Procedure for Analysis: 1- Support reaction 2- Shear & Moment Function  Specify separate coordinate x and associated origins, extending into regions of the beam between concentrated forces and/or couple moments or where there is a discontinuity of distributed loading.  Section the beam at x distance and from the free body diagram determine V from, M at section x

Example 4 Determine the internal shear and moment Function

Example 5 Determine the internal shear and moment Function

Example 6 Determine the internal shear and moment Function

Example 7 Determine the internal shear and moment Function

Shear and Moment diagram for a Beam