ANALYSIS AND DESIGN OF MAIN FRAME

In this design project the main frame which is situated close to the side wall is designed. The result of the design is considered being valid for all the main frames. The analysis and design is carried out with the ConSteel design software.

4.1 Design model 4.1.1 Structural model

The initial structural model of the examined main frame was created on the base of the

Preliminary Draw found in Fig. 9-11 of this Design Notes. The model was constructed on the 3D modeling window of the ConSteel software:

The eccentricities of the lateral supoports were neglected in the structural model. Supports were placed on to the reference axes and in the break points. The intermediate supports on columns and beams were placed at the middle points of the members. At the intermediate supports of the beams knee bars were assumed.

4.1.2 Cross-sectional models and properties of cross-sections

The models of cross sections were developed in the ConSteel software, and the cross-sectional properties were imported from the software.

4.1.2.1 Cross-section of columns

Knee bar Knee bar

Class of cross-section pure compression pure bending flange 1 1

web 4 1 Cross-sectional properties

- area [mm²] A c.pl 11424 A c.eff 10609

- moments of inertia [mm⁴] I c.y 518270000 I c.z 36884000 - sectional moduli [ mm³] W c.y.pl 2296600 W c.z.pl 460800 - St. Venant inertia moment [mm⁴] I c.t 729500

- warping constant [mm⁶] I c.w 2157000000000 4.1.2.2 Cross-section of beams

Class of cross-section pure compression pure bending flange 1 1

web 4 1 Cross-sectional properties

- area [mm²] A b.pl 9888 A b.eff 9346

- moments of inertia [mm⁴] I b.y 308197000 I b.z 36870000 - sectional moduli [ mm³] W b.y.pl 1677000 W b.z.pl 460800 - St. Venant inertia moment [mm⁴] I b.t 671166

- warping constant [mm⁶] I b.w 1358000000000 4.1.2.3 Cross-section of haunched beam

Haunch plates - flange: 240-20 - web: 310-6

The cross-section of the haunched beam is approximated by an I section where the intermediate flange is neglected. The height of the cross-section is considered in the theoretical corner of the frame.

Class of cross-section pure compression pure bending

- moments of inertia [mm⁴] I bh.y 1253000000 I bh.z 41472000 - sectional moduli [ mm³] W bh.y.pl 3716000 W bh.z.pl 518400 - St. Venant inertia moment [mm⁴] I bh.t 1017000

- warping constant [mm⁶] I bh.w 5191000000000 4.1.3 Material properties

- for cross-sectional resistances γ M0 1.0 f y0 f y γ M0

- for stability resistances γ M1 1.0 f y1 f y γ M1

5.1.3 Load model 5.1.3.1 General

The basic loads of the building were determined in Practice 2. Using these loads the design loads of the examined frame should be determined in this Chapter. The loads which have effect on the covering system (dead load of covering, snow load and wind load) are transmitted by the purlins as concentrated loads, see Figure 36a. If there are at least 3-4 purlins (wall beams) on the beam (column), the applied load may be considered as distributed load, see Figure 36b. In this design project distributed load is suggested applying.

5.1.3.2 Adequate frame to design

The wind load on the roof is changing from zone to zone. Therefore the frames of the building have different design loads. The greatest wind effect can be found on the frames at the end walls of the building but the width of the loading area is only the half of the frame distance.

Generally, it is for safe and economical design if the second frame is examined, as it is shown in Figure 37.

5.1.3.3 Load groups and load cases

The design software supports the generation of the load combinations. In order to use this tool the load cases should be collected into load groups. Load group contains load cases which

Fig.36 Loads on the main frame transmitted as:

(a) concentrated loads; (b) distributed load

Fig.37 Adequate frame and width of loading area for design (top view of the building)

belong to same load type (ex. snow, wind) and may neglect each others in the load combinations. Load case contains load items which act together in the same time (ex. cross wind loads on the frame). In this design project the following load groups and load cases are suggested applying:

• Dead loads

o Weight of structural members (WSM)

o Weight of covering system (WCS)

o Installation loads (IL)

• Snow load

o Totally distributed

o Non symmetrically distributed (left sided)

o Non symmetrically distributed (right sided)

Uniform intermediate frames Frame at wall

Adequate frame for design

Width of loading area (a)

(b)

• Wind load

The weight of the members of the frame is considered by the software. The user should select the load case which will contain this load (WSM). The weight of purlins, wall beams and covering layers may be collected into an individual load case (WCS). The installation loads (equipments, lightings, and so on) can be collected into another load case (IL). In this project the following dead load cases are suggested using (see Figure 38):

o WSM: p_g,s [kN/m] (loads considered by the software)

(where ’r’ denotes ’on roof’ and ’w’ denotes ’on wall’)

Snow load

The snow load is gravity load which means that it acts vertically. The basic snow load is related to 1 m² horizontal area. The snow load cases are illustrated in Figure 39. In this design project it is enough to take the totally distributed load (Case 1) into consideration. It is noted that in cases of unsymmetrical duopitch roofs the unsymmetrical load cases may be adequate. The frame is loaded by the following totally distributed snow load:

s c p_s =µ₁⋅ ⋅

where s [kN/m²] was determined in Practice 2, η1 is a factor given in Section 2.2.1.1. This snow load case is related to horizontal surface. The reduction of this load may be neglected for the safe, see Figure 40.

w

Case 1: Totally distributed Case 2: Unsymmetrical (left) Case 2: Unsymmetrical (right)

Fig.39 Snow load cases

Fig.40 Model of totally distributed snow load

Wind load

The wind may affect on the external and the internal surfaces of the building. The loads due to the wind effect may be calculated as following:

- external wind load: p_w,e =c_sc_d⋅c⋅w_e - internal wind load: p_w,i =c⋅w_i

where c_sc_d is the structural factor, which is 1.0 for buildings being not higher than 15 m. In this design project it is suggested applying the following wind load cases:

• Cross wind effect (θ=0°), see Annex 7

• Cross wind effect “+” internal wind effect, see Annex 8a

• Longitudinal wind effect (θ=90°), see Annex 8b

• Longitudinal wind effect “+” internal wind effect, see Annex 8c

It can be seen that a wind load case might have more cases. The number of cases (number of design load combinations) may be reduced neglecting the non adequate load cases.

Unfortunately, there are no general rules how to reduce the number of load cases.

5.1.3.4 Design load combinations

Design load combinations for transient and persistent design situations (basic combinations) are given by the following expressions (EN 1990 6.4.3.2 6.10):

s

1⋅c⋅ η

µ1 µ1

0.5µ1

µ1

0.5µ1

∑

∑

where

γG is the partial factor for dead loads (normally: 1,35) γQ,i partial factor for load case ’i’ (snow and wind load: 1,5)

Ψ0,i combination factor for load case ’i’ (snow load: 0,5; wind load: 0,6) These load combinations can be generated by

• Automatically

• Engineer

Generation of all the possible load combinations is supported by the software. This automatic method has some disadvantages:

- second order and stability analysis (it is suggested) should be executed for all of the load combinations (superposition must not applied);

- results may be reviewed difficultly;

- runtime may be considerable.

Method of generation by Engineer is preferred by senior engineers since using simple considerations (neglecting the non adequate load cases and combinations) the analysis may be executed and the results can be reviewed more easily. In this design project it is suggested using the two methods together: all the possible load combinations can be generated by the software, and then the inadequate load combinations may be disclosed.

5.1.3.4 Application

The example below shows the creation of the load model using ConSteel design software.