# Structural Mechanics 5 REACTIONS, SFD,BMD – with multiple loads

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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

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

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

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!

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

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

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