验证例题57.pdf

1Example 57 Title Rahmen(plate-frame)bridge subjected to a moving load(Moving Laod Module available upon request)Description Analyze a rahmen(plate-frame)bridge under a moving load.Find the maximum moments.Refer to the figure shown below.Structural geometry and analysis model Verification Example 2Model Analysis Type 3-D moving load analysis Unit System m,tonf Dimension Length 18 m Element Plate element(Thick type)Material Concrete Modulus of elasticity E =2.1 106 tonf/m2 Poissons ratio =0.167 Section Property Thickness Upper plate 0.25 m Pier and abutment 0.30 m Boundary Condition Nodes76 80,91 95 and 106 110;Constrain all DOFs.(Fixed supports)Load Case Moving loads DB-24 and DL-24 specified in the MOCT standard specification for bridges are applied.Example 57 3Results Displacements Verification Example 4 Mxx influence surface diagram for the element 15 due to DB-24(k-node)Mxx influence surface diagram for the element 18 due to DB-24(k-node)Example 57 5 Maximum positive moment of the structure in the X direction due to DB-24(Mxx)Maximum negative moment of the structure in the X direction due to DB-24(Mxx)Verification Example 6Comparison of Results Calculation of the maximum negative and positive moments Mxx for the structure Maximum positive moment:Nodes 30;occurs at the element due to DB-24 Maximum positive moment of the element (Node 30)Calculation of the positive moment Mxx due to DB-24 Mxx=(Concentrated load Value of the moment influence surface Impact coefficient)=(4.8 0.005222+19.2 0.005832+19.2 0.005832)1.300 =8.632 tonfm Positive moment Mxxdue to DL-24 Mxx=(Area of positive moment Value of the moment influence surface Unniform load+Value of the moment influence surface of maximum positive moment Concentrated load(for moment calculation)Impact coefficient =(2.23185 0.423333+0.33871 10.8)1.300 =5.984 tonfm Maximum positive moment:8.632 tonfm Maximum negative moment:Node 33;occurs at the elements due to DB-24 Calculation of the maximum negative moment of the element (Node 33)Positive moment Mxxdue to DB-24 Mxx=(Concentrated load Value of the moment influence surface Impact coefficient)=(4.8 -0.055892+19.2 -0.26602+19.2 -0.143618)1.300 =-10.573 tonfm Positive moment Mxxdue to DL-24 Mxx=(Area of negative moment Value of the moment influence surface Uniform load+Value of the moment influence surface of maximum negative moment Concentrated load(for moment calculation)Impact coefficient =(-4.1477 0.423333+-0.26602 10.8)1.300 =-6.04175 tonfm Maximum negative moment:-10.573 tonfm Example 57 7 Unit:m,tonf Moment due to DB-24 Moment due to DB-24 Result Location (Element-Node)MomentLocation(Element Node)MomentPositive-30 8.632-30 5.984 Maximum moment(Mxx)Negative-33-10.573-33-7.023 Positive-30 6.190-30 4.130 Maximum moment(Mxx)Negative-33-1.750-33-1.170 Positive-33 9.448-33 7.691 Maximum shear force(Vxx)Negative-33-9.448-33-7.691 Positive-49 3.943-30 3.509 Maximum shear force(Vxx)Negative-30-3.943-30-3.509 Positive5 0.0013365 0.005841Maximum vertical displacement(Dz)Negative30-0.00118430-0.009358Positive93 12.250193 10.1488Maximum vertical reaction(Fz)Negative78-0.258978-0.2519 Reference “Standard Specification for Bridges”,MOCT(Korean Ministry of Construction and Transportation),1996