ANALYSIS OF THE MAIN FRAME AND DESIGN OF THE CROSS- CROSS-SECTIONS
Step 4: Execute full analysis
5.3 Design of cross-sections .1 General
The aim of the cross-section design is to find the optimal structural dimensions. Dimensions of cross-sections may be optimal if they satisfy the design equations of resistances and the structure has the less cost (in this case the less weight) as possible. Design of cross-section is an iterative procedure, where the initial cross-sections are checked, the results are discussed, and some initial cross-sectional parameters may be modified. Any change in cross-sectional dimensions leads to change of the static model and the design forces as well. Theoretically, new analysis should be executed if there is any change in the model. Practically the new analysis may be neglected if the change is relatively inconsiderable.
It is important to consider that the resistances of members are usually determined by reduction of the cross-sectional resistances. Therefore the cross-sections can not be designed for 100%
usage of their resistances. In case of relatively stiff frames made from hot-rolled or equivalent welded profiles the usage of cross-sectional resistances can not be greater than 80-90%. In case of relatively slender frames (welded and tapered frame with large span) this limit may be 70-80%.
The EC3-1-1 provides multilevel design formula to determine the resistances of cross-sections. In general the resistance of a cross-section may be determined by one of the following design formulas:
• general elastic formula (based on design stresses)
• conservative interaction formula (based on design forces)
• plastic interaction formula (based on design forces and plastic properties)
The theoretical background of these design formulas was the subject of the previous studies (Steel I and Steel II).
5.3.2 Choosing design formula
The appropriate design formula depends on the type of the structure. Some guidelines are given below:
Hot-rolled or equivalent welded profiles
In the present design project HEA and IPE profiles with middle depth may be applied.
These cross-sections belong to Class 1 or 2 for pure bending and Class 2 or 3-4 for pure compression of the web. IPE profile may be Class 3-4 if the depth is greater than 400 mm and it is purely compressed. Frame which is composed of these types of profiles may be usually designed by plastic interaction formula where the effect of normal and shear forces reduce the bending moment resistance. Alternatively conservative interaction formula can be used (see the next paragraph).
Welded cross-section with relatively thin web
Welded cross-sections with relatively thin webs and IPE profiles with depth is grater than 400 mm belong to Class 1 or 2, if the flanges are considered and Class 3 or 4, if the web is considered for pure compression. If the normal and shear forces are relatively low, the conservative interaction formula may be used. In this case Aeff and Wpl.y may be used together in the same formula.
Welded cross-sections with high depth and thin web
Frames with relatively large span are usually made from welded cross-sections composed of relative slender web plate (large depth and thin plate). In this case the web of the cross-section may belong to Class 3 or 4, while the flanges belong to Class 2 or 3. This type of cross-sections can be designed by the general elastic formula where the effect of shear stresses is considered. The pure normal stresses can be calculated with elastic cross-sectional properties of the nominal and the effective cross-section, respectively. The effective cross-sectional properties are suggested calculating by software tool which assumes the interaction of the normal stresses due to pure axial force and due to pure bending moment (see the ConSteel/Section module).
5.3.3 Application
The application shown below illustrates the ‘hand’ design of the cross-sections and compares the results with those are given by the ConSteel software. Annex 11 contains the application guide on how to use the ConSteel program designing cross-sections.
4.4 Design of cross-sections
4.4.1 Relevant cross sections and design forces Relevant cross-sections to design
- Section K1: cross-section of column at columnbase - Section K2: cross-section of column at frame corner - Section K3: cross-section of beam at frame corner
- Section K4: cross-section of beam at maximum positive bending moment
Design forces of relevant cross-sections, see 4.3.1-2.
member cross-section LC design forces
moment [kNm] normal force [kN] shear force [kN]
column K1 4 M K1.y.Ed 354.36 N K1.Ed 179.66 V K1.Ed 116.73
K2 4 M K2.y.Ed 491.76 N K2.Ed 170.99 V K2.Ed 114.25
beam K3 4 M K3.y.Ed 469.56 N K3.Ed 142.20 V K3.Ed 148.56
K4 4 M K4.y.Ed 177.91 N K4.Ed 115.75 V K4.Ed 4.18
4.4.2 Design of cross-secctions Checking shear force effect
- maximum design shear force [kN] V max.Ed VK3.Ed V max.Ed 148.56= - minimum design shear area [mm2] A min.V h bw t bw. A min.V 2.20810= . 3
- pure shear resistance [kN] V min.Rd A min.Vf y0 3
. 1
1000 .
V min.Rd 299.576= Maximum design shear force does not excced 50% of shear resistance of web anywhere, Vmax.Ed<0.5Vmin.Rd ,
therefore effect of shear force may be neglected in any case.
Beam and column cross-sections are related to Class 4 for pure compression and Class 1 for pure bending. Therefore conservative interaction formula is used. Effective cross-sectional area is used for pure compression and plastic moduli for pure bending.
Dimensional factors (change kN to N and kNm to Nmm)
β N 1000 β M 1000000
Usage of resistance of the cross-section at top of the column excedes 90% as a practical limit. Instead of reinforcment of column cross-section design bending moment is taken at the buttom flange of the haunch beam, where thecolumn has realistic cross-section.
- decreasing of bending moment
- reduced design bending moment
M K2.y.Ed.red M K2.y.Ed ∆M M K2.y.Ed.red 430.329=
- Column Section K2
Cross-section checking was executed by the ConSteel software too (see the picture berlow). Results are basically the same than those of the hand calculation.
4.4.3 Applied cross-sections
Column section flange width [mm] 240
thickness [mm] 16
web width [mm] 368
thickness [ mm] 6
Beam section flange width [mm] 240
thickness [mm] 16
web width [mm] 468
thickness [mm ] 8
Haunch flange width [mm] 240
thickness [m m] 16
web width [mm] 300
thickness [mm] 6