Lecture 30: Examples on Method of Sections ENGI 1313 Mechanics I Lecture 30: Examples on Method of Sections

Lecture 30 Objective to illustrate the method of sections by example

Example 30-01 The Howe bridge truss is subjected to the loading shown. Determine the force in members DE, EH, and HG, and state if the members are in tension or compression.

Determine the force in truss members DE, EH, and HG Example 30-01 (cont.) Determine the force in truss members DE, EH, and HG Cut Along Section? Truss chords ED EH GH What Section to Use? Right Calculate Support Reaction Forces? Yes, at G

Determine the force in truss members DE, EH, and HG Example 30-01 (cont.) Determine the force in truss members DE, EH, and HG Support Reaction G What equilibrium equation? Gy

Determine the force in truss members DE, EH, and HG Example 30-01 (cont.) Determine the force in truss members DE, EH, and HG Draw Section FBD Assume all truss member forces are in tension Gy FED 40kN FEH FGH Gy

Determine the force in truss members DE, EH, and HG Example 30-01 (cont.) Determine the force in truss members DE, EH, and HG Equilibrium Equation? Gy FED 40kN FEH FGH Gy

Example 30-02 Determine the force in members OE, LE, and LK of the Baltimore truss and state if the members are in tension or compression.

Determine the force in truss members OE, LE, and LK Example 30-02 (cont.) Determine the force in truss members OE, LE, and LK Where to Start? What are the key truss joints (nodes)? Joint E Joint L Any particular characteristics? 5 unknowns @ E Zero-force @ L

Determine the force in truss members OE, LE, and LK Example 30-02 (cont.) Joint FBD at L FLE FLK FLM L

Determine the force in truss members OE, LE, and LK Example 30-02 (cont.) Section Cut? Draw FBD Examine FBD Known? Unknown? To Be Determined? Ay Ax E FML FOE FDE

Determine the force in truss members OE, LE, and LK Example 30-02 (cont.) Next Step? Reduce unknowns Find what support reaction? Ay What equilibrium equation? Ax Ay Ay Ax E FML FOE FDE

Determine the force in truss members OE, LE, and LK Example 30-02 (cont.) Support Reaction Ay Ax Ay

Determine the force in truss members OE, LE, and LK Example 30-02 (cont.) Next Step? Find FML What equilibrium equation? Ay = 6.375kN Ax E FML FOE FDE

Determine the force in truss members OE, LE, and LK Example 30-02 (cont.) Next Step? Find FOE What equilibrium equation? Ay = 6.375kN Ax E FML FOE FDE

References Hibbeler (2007) http://wps.prenhall.com/esm_hibbeler_engmech_1