268
Index
magnification factor 213–15, 218–19 mass 186, 211 mass-spring-damper system 186, 244–7, 249–50 mode shape 192, 202, 203 mode superposition 196 modulus of elasticity 67, 116 momentum 159 motion 186, 211 natural frequency 185–6, 196–9, 203–4 to displacement 196–8 to tension force 198–9, 203–4 natural period 185 neutral plane, neutral axis 32, 38, 42 normal force 61–6 parallel-axis theorem 29, 32 pendulum 170–84, 199 phase angle 214–17 pin-jointed structure 79–87 pinned support 4 prestress 127–38 centrally applied 128 demonstration 133–4 eccentrically applied 128–30 externally applied 130–2 practical examples 134–7 Raleigh Arena 107–8 relationship between natural frequency and displacement 196–8 between natural frequency and tension force 198–9, 203–4, 208–9 resonance avoidance 225–6 effect 221–2 footbridge 223–5 SDOF system 221 washbowl 228–9 resonance frequency 219–20 resonance testing 227–8 second moment of area 28–35 shape function 193–5 shear force 38–41 shear modulus 50, 118 shear stress 47–60 in bending 47–9 effect 53–60 in torsion 47, 49–52 sign convention 68 simple harmonic motion 211 simply supported beam 5, 39–42, 192–5 single-degree-of-freedom system 186–91, 211–23
smaller internal forces 96–112 cable-stayed bridge 111 floor structure 111–12 pair of rubber rings 105–6 Raleigh Arena 106–7 Zhejiang Dragon Sports Centre 108–9 spider’s web 135–7 stable and unstable equilibria 6 stiffness 79–81, 191–6 at critical point 79 at point 79 lateral 81 modal 191–6 strain energy bending 79, 81, 163 tension and compression 79 stress normal stress due to bending 30 normal stress due to tension and compression 61–6 shear stress due to bending and torsion 47–51 stress distribution 62–6 balloons on nails 62–3 flat shoes vs high-heel shoes 64–5 the Leaning Tower of Pisa 65–6 uniform and non-uniform 63 structure factor 141–9 strut 115–21 superposition 70, 196 support fixed 4 pinned 4 roller 4 suspended system 170–84 effect of added mass 178–80 floor 182–3 generalised 172–6 inclined suspended wood bridge 182 natural frequency 171–80 rotational 176–80 static behaviour 180–1 translational 176–80 tension 127–37 tension structure 137 torque 49–53 torsion 49–53 circular section 50–1 non-circular section 50–3 transmissibility 218 trusses 79 tuned-liquid-damper 247 tuned-mass-damper 244–7, 249–51 two-degrees-of-freedom system 244–7, 254–61