chapter  1
Introduction
Pages 12

A Cross-sectional area, plan area of bearings, accidental action Aa Cross-sectional area of structural steel Ab Area of bottom reinforcement of slab Abh Area of bottom transverse haunch reinforcement Ac Cross-sectional area of concrete Ac,eff Effective area of compression flange Acp Partial area of concrete Ac,tot Total area of concrete flange Act Area of tension zone before cracking Aeff Effective cross-sectional area due to plate buckling AE Seismic action Anet Net section area at holes Ap Gross area of plate Ar Reduced area of elastomeric bearings Aref Reference area for wind force As Area of reinforcement Asl Gross area of longitudinal stiffener Asp Partial area of reinforcement As,tot Total area of reinforcement Asf Area of transverse reinforcement cutting a section As,min Minimum reinforcement area Asl,eff Effective area of longitudinal stiffeners At Area of top reinforcement of slab Av Shear area A1 Area of steel plates of elastomeric bearings C Concrete, creep of concrete, wind load factor, spring constant Dc Action due to replacement of bearings ∆l Elongation, contraction ∆σE2 Equivalent direct stress range for 2 · 106 cycles ∆τE2 Equivalent shear stress range for 2 · 106 cycles ∆σR Fatigue resistance to direct stresses ∆τR Fatigue resistance to shear stresses

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∆T Temperature difference ∆TM Linear temperature difference ∆TN Uniform temperature difference E Modulus of elasticity Ea Modulus of elasticity of structural steel Eb Compression modulus of elastomer Ec Modulus of elasticity of concrete Ec,28 Modulus of elasticity of concrete at 28 days Ecm Modulus of elasticity of concrete-mean value Ed Design value of the effects of actions Ed,dst Design value of the effects of destabilizing actions Ed,stb Design value of the effects of stabilizing actions ED Absorbed hysteretic energy Elcm Modulus of elasticity of lightweight concrete-mean value Es Modulus of elasticity of reinforcement F Force Fcr Critical concentrated load FRd Design buckling resistance to concentrated transverse forces FW Wind force G Weight, shear modulus, permanent action Ga Shear modulus of structural steel Gc Shear modulus of concrete G1 Self-weight G2 Superimposed dead weight Gset Permanent action due to settlement permanent action due to

settlement H Horizontal force, lateral force I Second moment of area (moment of inertia), length, influence length Inet Second moment of area of net section Ip Second moment of area of plate, polar second moment of area of

a stiffener Isl Second moment of area of stiffened plate IT Torsional constant of cross section IW Warping constant I1 Second moment of area of uncracked section I1,0 Second moment of area of uncracked section for short-term

loading I2 Second moment of area of fully cracked section I2,sa Second moment of area of fully cracked section (structural steel +

reinforcement) J Creep function, impact energy, torsional constant K Spring stiffness of bearings, stiffness of system Keff Effective stiffness L Length, span Le Distance between zero moments Leff Effective length for resistance to concentrated forces

(continued)

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Lf Influence length LM Load model LΦ Determinant length M Bending moment, mass Ma,el,Rd Elastic design moment resistance of steel girder Mcr Bending moment at cracking of concrete Mel Elastic moment resistance Mel,Rd Elastic design moment resistance MEd Design moment Mf,Rd Design bending resistance of cross section consisting of the

flanges only Mmax,f Maximum moments due to fatigue loading Mmax,f,Ed Maximum moments in the fatigue combination Mmin,f Minimum moments due to fatigue loading Mmin,f,Ed Minimum moments in the fatigue combination MN,pl,Rd Design bending resistance of cross section allowing for axial

forces Mperm Moments due to all actions in combination except fatigue traffic

loads Mpl Plastic moment Mpl,Rd Design plastic bending resistance Mpl,V,Rd Design plastic bending resistance allowing for shear forces MRd Design bending resistance Msh Primary shrinkage moment MT,Ed Design torsional moment Mx Torsional moment Mxp Uniform torsional moment Mxs Nonuniform torsional moment MI Moment from first-order theory MII Moment from second-order theory Mw Bimoment M1 Bending moment acting on noncracked composite section

(state 1) M2 Bending moment acting on fully cracked composite section

(state 2) N Axial force, number of cycles Nb,Rd Design buckling resistance Nc Axial force in concrete Nc,el Force in concrete at elastic resistance of steel girder Nc,f Force in concrete for full shear connection Ncr Euler buckling load, axial force at cracking of concrete Nc,Rd Design resistance to compression NEd Design axial force Nobs Number of lorries per year in the slow lane NEd Design axial force Nt,Rd Design resistance to tension Nu,Rd Design resistance to tension for sections with holes Npl,Rd Plastic design resistance force

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Ns Axial force in reinforcement Nsh Primary shrinkage axial force P Load, force, prestressing, permanent PT Secondary effects of creep and shrinkage PRd Shear resistance of shear connectors at ultimate limit state (ULS) PRd,ser Shear resistance of shear connectors at serviceability limit state (SLS) Q Variable action, traffic load Qik Axle load Qlk Braking force Qm1 Average gross weight of lorries in slow lane Qtk Centrifugal force Qvk Concentrated vertical force for rail traffic R Resistance, relaxation factor Rd Design resistance RH Relative humidity S Shrinkage of concrete, soil factor, static moment (first moment of

area), shape factor of bearings Sa,d Design response spectrum, design spectral acceleration Se Elastic response spectrum, elastic spectral acceleration Sw Sectorial area T Temperature, vibration period Tb Total thickness of elastomeric bearings Te Total nominal thickness of elastomeric layers Tq Total thickness of elastomeric layers including upper and lower layers TS Tandem system UDL Uniformly distributed load V Shear force, vertical load, train speed Vb,Rd Design shear resistance Vbf,Rd Design shear resistance contribution of the flange Vbw,Rd Design shear resistance contribution of the web VL Force due to longitudinal shear Vmax,f Maximum shear forces due to fatigue loading Vmin,f Minimum shear forces due to fatigue loading Vbw,Rd Shear buckling resistance VEd Design shear force Vpl,Rd Plastic shear resistance VRd Design shear resistance W Section modulus, wind load Weff Elastic section modulus of effective cross section Wel Elastic section modulus Wpl Plastic section modulus Φ Diameter of bars Φs* Maximum bar size for crack control

Φ2 Dynamic factor Φ3 Dynamic factor X Material property Z Through-thickness property

Examples

M1,Ed,0 Design (Ed) bending moment (M) acting on noncracked (1) composite section due to short-term (0) actions

Mel,Rd,∞ Long-term (∞) elastic (el) design (d) bending moment (M) resistance (R) σc,Ed,∞ Design (Ed) concrete (c) normal stress (σ) due to long-term (∞) actions

Structural Analysis Programs Used

• RSTAB (www.dlubal.com) • SOFISTIK (www.sofistik.com)