Determinate structures

A structure is determinate when it has

• 3 unknown forces applied to it

• 3 unknown support reactions

• 3 more moments than forces

• 3 supports

The 3 support reactions of a determinate structure can be calculated because there are 3 equations of ________________ available to use in the solution.

 $\Sigma\ F_x\ =\ 0\ ,\ \Sigma\ F_y\ =\ 0\ ,\ \Sigma\ M\ =\ 0$  

Without doing any calculations, determine the reactions R_A and R_B

• R_A = 6 kN, R_B = 4 kN

• R_A = 5 kN, R_B = 5 kN

• R_A = 7.5 kN, R_B = 2.5 kN

• R_A = 3.3 kN, R_B = 6.7 kN

We want to find the vertical reactions R_A and R_B.

First, ignore the 5 kN load.

What are the support reactions due to the 15 kN load alone?

• R_A = 7.5 kN up, R_B = 7.5 kN up

• R_A = 9 kN up, R_B = 6 kN up

• R_A = 8 kN up, R_B = 7 kN up

• R_A = 10 kN up, R_B = 5 kN up

We still want to find the vertical reactions R_A and R_B.

Now, ignore the 15 kN load.

What are the support reactions due to the 5 kN load alone?

• R_A = 1 kN up, R_B = 4 kN up

• R_A = 2 kN up, R_B = 4 kN up

• R_A = 2 kN down, R_B = 7 kN up

• R_A = 1 kN down, R_B = 6 kN up

So, due to the 15 kN load, R_A = 9 kN up, R_B = 6 kN up.

Due to the 5kN load alone, R_A = 1 kN down, R_B = 6 kN up.

Now we can calculate the total reactions by combining the reactions induced by the individual loads:

ANSWER

R_A = __ kN ____ , R_B = __ kN ____

(just type the missing numbers and words eg 5 down 6 up)

What are the support reactions R_A and R_B due to the 15 kNm moment?

• R_A = 10 kNm CW, R_B = 5 kNm CW

• R_A = 3 kN up, R_B = 2 kN up

• R_A = 3 kN up, R_B = 3 kN down

• R_A = 5 kNm CW, R_B = 1.7 kNm CW