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Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland ENGI 1313 Mechanics I Lecture 30:Examples on Method of Sections

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ENGI 1313 Statics I – Lecture 30© 2007 S. Kenny, Ph.D., P.Eng. 2 Lecture 30 Objective to illustrate the method of sections by example

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ENGI 1313 Statics I – Lecture 30© 2007 S. Kenny, Ph.D., P.Eng. 3 Example 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.

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ENGI 1313 Statics I – Lecture 30© 2007 S. Kenny, Ph.D., P.Eng. 4 Example (cont.) 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

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ENGI 1313 Statics I – Lecture 30© 2007 S. Kenny, Ph.D., P.Eng. 5 Example (cont.) Support Reaction G What equilibrium equation? GyGy Determine the force in truss members DE, EH, and HG

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ENGI 1313 Statics I – Lecture 30© 2007 S. Kenny, Ph.D., P.Eng. 6 Example (cont.) Draw Section FBD Assume all truss member forces are in tension GyGy F GH GyGy F EH F ED 40kN Determine the force in truss members DE, EH, and HG

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ENGI 1313 Statics I – Lecture 30© 2007 S. Kenny, Ph.D., P.Eng. 7 Example (cont.) Equilibrium Equation? GyGy F GH GyGy F EH F ED 40kN Determine the force in truss members DE, EH, and HG

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ENGI 1313 Statics I – Lecture 30© 2007 S. Kenny, Ph.D., P.Eng. 8 Example Determine the force in members OE, LE, and LK of the Baltimore truss and state if the members are in tension or compression.

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ENGI 1313 Statics I – Lecture 30© 2007 S. Kenny, Ph.D., P.Eng. 9 Example (cont.) Where to Start? What are the key truss joints (nodes)? Joint E Joint L Any particular characteristics? 5 E L Determine the force in truss members OE, LE, and LK

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ENGI 1313 Statics I – Lecture 30© 2007 S. Kenny, Ph.D., P.Eng. 10 Example (cont.) Joint FBD at L F LE F LK F LM L Determine the force in truss members OE, LE, and LK

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ENGI 1313 Statics I – Lecture 30© 2007 S. Kenny, Ph.D., P.Eng. 11 Example (cont.) Section Cut? Draw FBD Examine FBD Known? Unknown? To Be Determined? AyAy AxAx E Determine the force in truss members OE, LE, and LK F ML F OE F DE

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ENGI 1313 Statics I – Lecture 30© 2007 S. Kenny, Ph.D., P.Eng. 12 Example (cont.) Next Step? Reduce unknowns Find what support reaction? A y What equilibrium equation? AyAy AxAx AyAy AxAx E Determine the force in truss members OE, LE, and LK F ML F OE F DE

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ENGI 1313 Statics I – Lecture 30© 2007 S. Kenny, Ph.D., P.Eng. 13 Example (cont.) Support Reaction A y AyAy AxAx Determine the force in truss members OE, LE, and LK

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ENGI 1313 Statics I – Lecture 30© 2007 S. Kenny, Ph.D., P.Eng. 14 A y = 6.375kN AxAx E Example (cont.) Next Step? Find F ML What equilibrium equation? Determine the force in truss members OE, LE, and LK F ML F OE F DE

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ENGI 1313 Statics I – Lecture 30© 2007 S. Kenny, Ph.D., P.Eng. 15 A y = 6.375kN AxAx E Example (cont.) Next Step? Find F OE What equilibrium equation? Determine the force in truss members OE, LE, and LK F ML F OE F DE

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ENGI 1313 Statics I – Lecture 30© 2007 S. Kenny, Ph.D., P.Eng. 16 References Hibbeler (2007) mech_1

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