1. ME221Lecture 151 ME 221 Statics Lecture #15b Sections 6.1 – 6.4

2. ME221Lecture 152 Chapter 6: Analysis of Structures The knowledge of internal forces is a fundamental requirement for true design The Structural elements are: Trusses Frames Machines

3. ME221Lecture 153 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.

4. ME221Lecture 154 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.

5. ME221Lecture 155 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

6. ME221Lecture 156 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

7. ME221Lecture 157 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:

8. ME221Lecture 158 P Cy P Cx CyCy C  F CA F CB At Joint C:

9. ME221Lecture 159 P By P Bx B  F BA F BC At Joint B:

10. ME221Lecture 1510 Using Matrix Notation = Using manual calculations Look for joints with 2 unknowns

11. ME221Lecture 1511 Example

12. ME221Lecture 1512 Example 1.2 m 1.2 m 6 kN 3 kN E B A CD 0.9 m

13. ME221Lecture 1513 6 kN 3 kN E B A C D 44 16 4 4 9 9 15 5 5