Structural Mechanics Analysis and Diagrams
Explore detailed structural mechanics concepts and diagrams related to neutral axis, bending moments, shear forces, free-body diagrams, and more. Gain insights into analytical and finite element analysis results.
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y y Neutral axis x z A L F F y(dv/dx) y = dv/dx v(x) +Vy +M +M y x +P +P +Vy p d V y + d V x y y d x p(x) d d M x + d M x V M y C2 C3 x C1 F1 F2 F3 dx Free-body diagram p0 E,I,L
1.0 0.8 v(x)/vmax 0.6 0.4 v_exact v_approx. 0.2 0.0 0 0.2 0.4 0.6 0.8 1 x x 0.000 0.2 0.4 0.6 0.8 1 -0.04 M(x) -0.08 M_exact M_approx -0.12 0.6 V_exact V_approx 0.4 0.2 V(x) 0.0 -0.2 -0.4 -0.6 0 0.2 0.4 0.6 0.8 1 x p0 C E,I,L F
0.02 0.015 v(x) 0.01 v_exact v_approx. 0.005 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 x 1 (a) 500 M_exact M_approx. 400 300 M(x) 200 100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 x 1 (b) 500 400 Vy(x) 300 Vy_exact Vy_approx. 200 (c) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 x 1 F2 F1 C1 C2 x p(x) v2 v1 1 2 x L x2 x1 s = 1 s = 0
1.0 N1 N3 0.8 0.6 0.4 0.2 N2/L 0.0 0 0.2 0.4 0.6 0.8 1 N4/L -0.2 v1 v2 2 1 L y p(x) C1 C4 x C3 3 C5 5 C2 2 1 4 F1 1 x F2 = F3 = F4 = F5 ( ) 4 2 x ( ) 1 ( ) 1 2 ( ) 2 1 ( ) 2 2 ( ) 3 1 ( ) 3 2 ( ) 4 1 x x x x x x y 2EI x EI 3 2 1 2L L F2 F3
p Equivalent pL/2 pL/2 pL2/12 pL2/12 y x 1 2 3 1 m 1 m F2 = 240 N p0 = 120 N/m EI = 1000 N-m2 C = 50 N-m
0.000 FEM Exact -0.002 -0.004 v -0.006 -0.008 -0.010 0 0.2 0.4 0.6 0.8 1 x 0.000 FEM Exact -0.005 -0.010 -0.015 -0.020 -0.025 -0.030 0 0.2 0.4 0.6 0.8 1 x 10 FEM Exact 0 -10 -20 M -30 -40 -50 -60 0 0.2 0.4 0.6 0.8 1 x 120 FEM Exact 100 80 Vy 60 40 20 0 0 0.2 0.4 0.6 0.8 1 x
p L 0.35 v_analytical v_FEA 0.30 0.25 0.20 v(s) 0.15 0.10 0.05 0.00 0.0 0.2 0.4 0.6 0.8 1.0 s 0.00 M_Analytical M_FEA -0.05 -0.10 M(s) -0.15 -0.20 -0.25 -0.30 0 0.2 0.4 0.6 0.8 1 s 1.00 Vy_Analytical Vy_FEA 0.80 0.60 0.40 0.20 Vy(s) 0.00 -0.20 -0.40 -0.60 -0.80 -1.00 0 0.2 0.4 0.6 0.8 1 s
1 v 2 v 1 u u 1 q 2 2 q p u u 2 2 F 2 v 2 v 1 2 q 2 q 2 3 2 3 1 u 1 u 1 4 1 v 1 v 1 q 1 q Local coordinates 2 v u 2 y 2 q x 2 1 v 1 u y 1 q 1 Global coordinates x F 2 1 a y 2 45o 3 1 x a
0.12N 1390N 981N 2 18.3N 1.15Nm 1.15Nm 2 x y y x 1.11Nm 18.3N 1 4.33Nm 3 0.12N 1390N 981N 1000N 18N 983N 1.11Nm 4.33Nm 981N 981N
Fz2 x 1 1 2 2 2 2 y x z z 3 3 y y C P x L C P M(x) C P P v(x) x x d x dx x dx
7 Exact tip deflection Approx. tip deflection 6 P < 0 5 Tip Deflection 4 3 2 1 P > 0 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 L 3 2.5 2 v(x) [m] 1.5 1 0.5 0 0 0.2 0.4 0.6 0.8 1 x [m] v (P=0) v (P=+2000 N) v (P=-2000 N) 2.5 2 1.5 v(x) 1 0.5 0 0 0.2 0.4 0.6 0.8 1 x [m] Mode 1 Mode 2
y P x P 1m 1m 2m Mode 1 Mode 2 x (m)
Local coordinates 2 v u 2 y 2 q x 2 1 v f 1 u y 1 q 1 x Global coordinates P P 2 3 2 3 1 1 4 1.0 1.0 0.5 0.5 0 0 0 0 0.5 1.0 0.5 1.0
w w z h a a L y 1 2 3 4 x 1 2 3 4 5 0.2 0.1 1 2 3 4 5 0 Deflection -0.1 -0.2 v = 0.18246in -0.3 -0.4 -0.5 0 5 10 15 20 25 30 35 40 X
16.655" 1.68" 0.945" Centroid 36.74" 1.68" y y 11 F 10 10 9 L/2 x L/2 3 3 2 2 1 F x 1
20 2 500 1 Seat 400 3 325 20 y Unit: mm x 4 20 400 Pedal 825 6 5 50 1,000 N L = 1 m p0 y x C L p0 y x C L
1,000 N 0.5 m 1 m k A C 2h b B L F2 F2 1 C2 C2 1 2 1 2 E, I L P q LT f L = 1 m EI = 0.15 N m2 f = 1 N/m 1 2 L p0 1 2 3 p0 F L L
F E, I, L k C = 100 N-m 1 E, I 2 1 m k 3 F 2 1 E, I L k 3 1 2 L 10,000N 3 2 1 1mm 0.1m 0.1m
q0 F1 F2 L M1 y M2 x P F1 F2 L M1 y M2 x 0.5 m B 1 m 1 m 1,000 N C2 1 m 1 m 1 2 3 P 1 2 3 1 2 E, I, L E, I, L 3 1 2 E, I L L F y F= 60 N x 1 m 1 m
2 1 P C E, I, L q E=100 L=1 q=1 A=0.1 I=0.01 y 45o x F y R = 100 mm 10 mm x 10 mm F F/2 y R x
E2 2 3 E1 E3 1 4 2m 1m q 1m y 2m x 1 2 1 2 45o 3 P Q r = 0.05 1,000 N 0.025 0.025 R S
y 2 x P 3 1 1m 2m y 2 3 P 1m x 1 1m y 3 kT 1 x 1 2 kL 2 3 L 2 3 2 P P 3 1 1 4
q 2 x 1 E, I L F E, I 2 1 L ? ? 1 2 s 1
