ME221Lecture 281 ME 221 Statics Lecture #28 Sections 6.1 – 6.4

ME221Lecture 282 Homework #10 Chapter 7 problems: –2, 5, 6, 8, 19, 21, 24, 26 & 35 Due Friday, November 7

ME221Lecture 283 Homework #11 Chapter 6 problems: –2, 3, 6 & 7 – Method of Joints –32, 36, 47 & 53 – Method of Sections –68 & 75 – See Angel for info Due Wednesday, November 19

ME221Lecture 284 Quiz #6 Today Exam #3 Wednesday, November 12

ME221Lecture 285 Chapter 6: Analysis of Structures The knowledge of internal forces is a fundamental requirement for true design The Structural elements are: Trusses Frames Machines

ME221Lecture 286 Trusses Composed of slender straight pieces connected together by frictionless pins where all the loads (no moments) are applied. Each member will act as a two-force member (either in tension or compression). All the forces acting on a truss member are axial.

ME221Lecture 287 Frames Are designed to support, prevent or transmit loads (forces, no moments). At least one member is not a two-force member. Machines Are designed to transmit force, motion or energy (forces and moments). Will always have at least one member with multiple forces.

ME221Lecture 288 Planar Trusses If the planar truss (2-D) is statically determinant, then the number of joints is related to the number of reactions and internal members by : 2j = m + r j = number of joints m = number of internal members r = number of reactions

ME221Lecture 289 Analysis of Trusses Using the Method of Joints AyAy AxAx P Ax P AY P By P Bx P Cy P Cx CyCy A B C  We need to solve for: (1) - Internal forces F AB, F AC, and F BC (2) - Reactions A x, A y and C y

ME221Lecture 2810 AyAy AxAx P Ax P AY A  F AC F AB F AB cos  + F AC + A x = -P ax ……………….(1) F AB sin  + A y = -P ay ……………………(2) Joint A:

ME221Lecture 2811 P Cy P Cx CyCy C  F CA F CB At Joint C:

ME221Lecture 2812 P By P Bx B  F BA F BC At Joint B:

ME221Lecture 2813 Using Matrix Notation = Using manual calculations Look for joints with 2 unknowns

ME221Lecture 2814 Example

ME221Lecture 2815 Example 1.2 m 1.2 m 6 kN 3 kN E B A CD 0.9 m

ME221Lecture kN 3 kN E B A C D