1. Structural Mechanics 5 REACTIONS, SFD,BMD – with multiple loads
10 kN
20 kN
30 kN RA RB
1.50m
0.50m
2.00m
1.00m

2. Sum of moments about RA = 0
RB x ( ) = 10 x (1.50) + 20 x( ) + 30x( )
RB x (5.0) = 10 x (1.5) x(2.0) + 30x(4)
RB = {10 x (1.5) x(2.0) +30x(4)} / 5.0
RB = { } / 5.0
RB = {175} / 5.0
RB = 35kN
10 x (1.50)
+ 20 x( )
+ 30x( )
- RB x ( )
= 0
20 kN RA RB
30 kN
10 kN
1.50m
2.00m
0.50m
1.00m

3. Sum of moments about RB = 0
RA x ( ) - 10 x ( ) - 20 x( ) - 30x( 1.0)
RA x (5.0) = 10 x (3.5) x(3.0) + 30x(1.0)
RA = { } / 5.0
RA = {125} / 5.0
RA = 25kN

4. So likely that calculations are correct!
CHECK VERTICAL FORCES
UPWARD REACTION = RB + RA = = 60 kN
DOWNWARD FORCE = =60 kN
So likely that calculations are correct!

5. SHEAR FORCE DIAGRAM RB = 35kN RA = 25kN 10 kN 20 kN 30 kN 25kN
Space diagram SHEAR FORCE DIAGRAM
10 kN
20 kN
30 kN
RB =
35kN
RA =
25kN
25kN
=15kN =0
= -5kN
= -35kN

6. BENDING MOMENT DIAGRAM
Space diagram
10 kN
20 kN
30 kN
RA =
25kN
RB =
35kN
1.50m
0.50m
2.00m
1.00m
45.0kNm
37.5kNm
35.0kNm
0kNm
Section 1
Section 2
Section 3

7. BMD CALCULATIONS Section 1 25kN [1.5]m = 37.5 kNm Section 2
25kN [ ]m -10kN[0.5]m = 45.0kNm
(NB max BM where shear force crosses the zero axis)
Section 3
25kN [ ]m -10kN [ ]m-20kN[2.0]m = 35.0kNm
Check: (taking BM from the RHS)
35kN [1.0]m = 35.0kNm