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Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland ENGI.

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Presentation on theme: "Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland ENGI."— Presentation transcript:

1 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

2 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

3 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.

4 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

5 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

6 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

7 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

8 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.

9 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

10 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

11 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

12 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

13 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

14 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

15 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

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


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