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 (1.5 +0.5 +2.0 +1.0) = 10 x (1.50) + 20 x(1.5 +0.5) + 30x( 1.5 +0.5 +2.0) RB x (5.0) = 10 x (1.5) + 20x(2.0) + 30x(4) RB = {10 x (1.5) + 20x(2.0) +30x(4)} / 5.0 RB = {15 + 40 + 120 } / 5.0 RB = {175} / 5.0 RB = 35kN 10 x (1.50) + 20 x(1.5 +0.5) + 30x( 1.5 +0.5 +2.0) - RB x (1.5 +0.5 +2.0 +1.0) = 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 (1.5 +0.5 +2.0 +1.0) - 10 x (0.5+2.0+1.0) - 20 x(2.0 +1.0) - 30x( 1.0) RA x (5.0) = 10 x (3.5) + 20x(3.0) + 30x(1.0) RA = {35+60+30} / 5.0 RA = {125} / 5.0 RA = 25kN

So likely that calculations are correct! CHECK VERTICAL FORCES UPWARD REACTION = RB + RA = 35 + 25 = 60 kN DOWNWARD FORCE = 10+20+30 =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 25 -10 =15kN -35 +35 =0 15 -20 = -5kN -5 -30 = -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 [1.5+0.5]m -10kN[0.5]m = 45.0kNm (NB max BM where shear force crosses the zero axis) Section 3 25kN [1.5+0.5+2.0]m -10kN [2.0+0.5]m-20kN[2.0]m = 35.0kNm Check: (taking BM from the RHS) 35kN [1.0]m = 35.0kNm