Structure Analysis I Lecture 7 Internal Loading Developed

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 Determine the internal shear and moment acting in section 1 in the beam as shown in figure 18 k. N 6 k. N

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