1. CE 201 - Statics Lecture 2

2. Contents Vector Operations – Multiplication and Division of Vectors – Addition of Vectors – Subtraction of vectors – Resolution of a Vector Vector Addition of Forces Analysis of Problems

3. Vector Operations Multiplication and Division of a Vector by a Scalar Vector A Scalar a A  a = aA Magnitude of aA Direction of A if a is positive (+) Direction of –A (opposite) if a is negative (-) A -A 1.5 A

4. Vector Addition Vectors are added according to the parallelogram law The resultant R is the diagonal of the parallelogram If two vectors are co-linear (both have the same line of action), they are added algebraically A B A B R = A + B A B B A A B

5. Vector Subtraction The resultant is the difference between vectors A and B A B -B A R R A

6. Resolution of a Vector If lines of action are known, the resultant R can be resolved into two components acting along those lines (i.e. a and b). a b A B R

7. Vector addition of Forces Force! Is it vector OR scalar? Why? The two common problems encountered in STATICS are: 1. Finding the RESULTANT (by knowing the COMPONENTS). OR 2. Resolving a FORCE into its COMPONENTS (by applying the parallelogram law). If more than two forces are to be added!! Apply the same law more than once depending on the number of forces.

8. 3 Forces F1 F2 F3 R1=F1+F2 R2=R1+F3

9. Four Forces F1 F2 F3 R1=F1+F2 R2=R1+F3 F4 R3=R2+F4

10. Analysis of Problems Two procedures to be followed: Parallelogram law Trigonometry sine and/or cosine laws may be used

11. Sine Law A/sin (a) = B/sin (b) = C/sin (c) a A B b C c

12. Cosine Law C =  A 2 +B 2 -2ABcos (c) a A B b C c

13. Examples 2.1 2.2 2.3 2.4 Problem 2-8 Problem 2-25