EF 202, Module 3, Lecture 1 Trusses - 1 EF Week 9

EF 202, Module 3, Lecture 1 2 Truss - Definition A truss is a framework of members joined at ends with frictionless pins to form a stable structure. Basic shape is a triangle.

EF 202, Module 3, Lecture 1 3 Truss Bridges Knoxville Railroad Bridges Highway Bridge CSX Norfolk Southern

EF 202, Module 3, Lecture 1 4 Joints Pinned JointRiveted Joint Frictionless pin is good assumption if members concentric.

EF 202, Module 3, Lecture 1 5 Types of Truss Named after inventor: HowePratt Named after railroad company: Baltimore

EF 202, Module 3, Lecture 1 6 Methods of Truss Analysis Method of joints (today) Method of sections (next week)

EF 202, Module 3, Lecture 1 7 Method of Joints - Concepts Draw FBD’s of pins. Show forces acting on pins (not forces acting on members). Concurrent, coplanar systems. Two independent equations (force summations) at each pin. No more than two unknowns at a pin.

EF 202, Module 3, Lecture 1 8 The method of joints does not employ moment summations. No-No

EF 202, Module 3, Lecture 1 9 Method of Joints - Steps 1. Solve for structure’s overall support reactions. Follow process for nonconcurrent, coplanar system. 2. Start at a joint with 1 or 2 unknowns. Follow process for concurrent, coplanar system. 3. Repeat step 2 as necessary.

Example – Method of Joints Given: Required: Force in each member using method of joints lb 1000 lb 6 ft10 ft 8 ft A B C D E

1. Solve for support reactions of whole structure lb 1000 lb 6 ft10 ft 8 ft A B C D E 2000 lb 1000 lb 6 ft10 ft 8 ft A B C D E EyEy ExEx CxCx x y +

2000 lb 1000 lb 6 ft10 ft 8 ft A B C D E 3000 lb 5250 lb 2. Draw FBD of Joint A. x-comp.y-comp.  00 x y +

2000 lb 1000 lb 6 ft10 ft 8 ft A B C D E 3000 lb 5250 lb 2. Draw FBD of Joint B. x-comp.y-comp.  00 x y +

2000 lb 1000 lb 6 ft10 ft 8 ft A B C D E 3000 lb 5250 lb 2. Draw FBD of Joint D. x-comp.y-comp  1500   1000  00 x y +

2000 lb 1000 lb 6 ft10 ft 8 ft A B C D E 3000 lb 5250 lb 2. Draw FBD of Joint E. x-comp.y-comp F EC  00 x y +

2000 lb 1000 lb 6 ft10 ft 8 ft A B C D E 3000 lb 5250 lb 2. Draw FBD of Joint C. x-comp.y-comp  00 x y +

2000 lb 1000 lb 6 ft10 ft 8 ft A B C D E 1500 lb T 5250 lb C 3000 lb C 1000 lb C 4800 lb T 2500 lb C

EF 202, Module 3, Lecture 1 18 Bonus! Some truss members carry no force and are called zero-force members. (See section 6-6 in the text.) Some structures are externally statically indeterminate. (See Online Homework )