375x
001027
2024-02-28

VE 1027 | Capacity Design for Beam According to DIN EN 1998-1

In this verification example, the capacity design values of shear forces on beams are calculated in accordance with EN 1998-1, 5.4.2.2 and 5.5.2.1 as well as the capacity design values of columns in flexure in accordance with 5.2.3.3(2). The system consists of a two span reinforced concrete beam with a span length of 5.50m. The beam is part of a frame system. The results obtained are compared with those in [1].


Material Concrete C20/25 Modulus of Elasticity E 30000 N/mm2
Design value of concrete compressive strength fcd 11.333 N/mm2
Reinforcing Steel B400S(C) Modulus of Elasticity Es 200000.000 N/mm2
Design yield strength fyd 347.826 N/mm2
Geometry Structure Beams length lb 5.500 m
Columns length lc 4.000 m
Beams cross-section Height h 550 mm
Width b 300 mm
Concrete cover cnom 20 mm
Columns cross-section Height h 500 mm
Width b 300 mm
Concrete cover cnom 22 mm
Loads Permanant loads Dead Load LC1 10.875 kN/m
Dead Load LC1 571.900 kN
Dead Load LC1 158.650 kN
Imposed loads Live Load LC2 20.000 kN/m
Dynamic loads Modal LC3
Response Spectrum LC4

RFEM Settings

  • the ductility class of the model is set to high ductility (DCH)

Results

  1. Capacity Rule for Shear - Capacity design values of shear forces on beams acc. to EN 1998-1, 5.4.2.2 and EN 1998-1, 5.5.2.1

    The design check capacity rule for bending is carried out at the face of the supports A and B.
    Capacity Rule for Shear- Capacity design values of shear forces on beams acc. to EN 1998-1, 5.4.2.2 and EN 1998-1, 5.5.2.1
    Parameter Description Unit RFEM Reference Solution Ratio
    M+Rd,1,y Positive (sagging) moment resistance of member at start section [kNm] 119.301 118.700 1.00
    M-Rd,1,y Negative (hogging) moment resistance of member at start section [kNm] 86.096 85.800 1.00
    M+Rd,2,y Positive (sagging) moment resistance of member at end section [kNm] 119.290 118.700 1.00
    M-Rd,2,y Negative (hogging) moment resistance of member at end section [kNm] 169.321 168.800 1.00
    lcl Clear span of beam [m] 5.100 5.100 1.00
    VA,g+ψ2q,max Shear force due to quasi-permanent loads for simply supported beam in the face of the support A [kN] 53.550 53.550 1.00
    V-A,Ed,max,z Shear force corresponding to maximum negative end moment in z-direction [kN] -14.361 -14.100 1.02
    V+A,Ed,max,z Shear force corresponding to maximum positive end moment in z-direction [kN] 101.876 101.670 1.00
    ζ1,max Ratio of design shear forces V-Ed,max / V+Ed,max for result combination [-] -0.141 -0.139 1.01
    VB,g+ψ2q,max Shear force due to quasi-permanent loads for simply supported beam in the face of the support B [kN] 53.550 53.550 1.00
    V-B,Ed,min,z Shear force corresponding to minimum negative end moment in z-direction [kN] -121.461 -121.200 1.00
    V+B,Ed,min,z Shear force corresponding to minimum positive end moment in z-direction [kN] -5.224 -5.430 0,96
    ζ2,min Ratio of design shear forces V+Ed,min / V-Ed,min for result combination [-] -0.043 -0.045 0.95

  2. Capacity Rule for Bending - Capacity design of columns in flexure acc. to EN 1998-1, 5.2.3.3(2)

    Capacity Rule for Bending - Capacity design of columns in flexure acc. to EN 1998-1, 5.2.3.3(2)
    Parameter Description Unit RFEM Reference Solution Ratio
    M-Rd,c,y,9 Negative moment resistance of column 9 at support B [kNm] -286.909 -281.000 1.02
    M-Rd,c,y,6 Negative moment resistance of column 6 at support B [kNm] -293.171 -295.000 0.99
    ΣM-Rd,c,y Sum of moment resistances of columns at node B [kNm] -580.080 -576.000 1.00
    M+Rd,b,y,1 Positive moment resistance of member 1 at the left side of node B [kNm] -169.321 -168.800 1.00
    M+Rd,b,y,2 Positive moment resistance of member 2 at the right side of node B [kNm] -119.804 -118.700 1.01
    ΣM-Rd,b,y Sum of moment resistances of beams at node B [kNm] -289.125 -287.500 1.02
    η+y Design check ratio of positive capacity moments [-] 0.648 0.649 0.99

References
  1. Mekouris, Constantine; Butenweg, Christoph, Concrete Yearbook 2008. Chapter V: Earthquake-resistant design of structures according to DIN 4149:2005 Berlin: Ernst & Sohn 2008


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