Medupi loco-shed

Girder Design

Designer: Dane van Tonder

Date: 09 September 2015

Checked by:

Revision: 00

Code Ref

Calculation

Result

Material Constants

Structural steel - S355JR:

Bearing Strength:

Youngs Modulus:

Bolts Grade 8.8:

Tension Strength:

Shear Strength:

Ultimate strenght:

Bearing Strength:

Weld Strength:

Poisson's Ratio:

Shear Modulus:

Material Factor:

Check at Eaves:

Load reactions for rafter section haunched by the column

Worst case is taken as Load case 132 (DL+Wind1-2+Crane stat)

Node 20(node closest to column):

Node 22:

Properties of 356x171x45 UB:

Depth of Rafter:

Width of Rafter:

Flange thickness:

Web thickness:

Radius at web:

Rafter Area:

Rafter Moment of inertias:

Section Moduli of rafter:

Radius of gyration of rafters:

Plastic moduli:

Saint Venant Constant:

Warping Constant:

Properties of the Haunch

The Haunch properties are calculated at section A-A, which is perpendicular to the Haunch

Total Depth of Haunch at Column face:

Total depth of Haunch at section A-A:

Flange of Rafter

Flange thickness:

Web thickness:

Radius at web:

Haunch Depth:

Haunch web area:

Haunch bottom flange area:

Total area of section:

Distance:

Distance:

Distance:

Section Neutral axis:

Properties of Hauch at Section A-A:

Moment of Inertia :

Section Moduli :

Radius of Giaration r.x:

Moment of Inertia Iy:

Section Moduli Zy:

Radius of Giaration ry:

Saint Venat Constant:

Warping Constant Middle Flange Ignored

Plastic Section of Haunch (ignore middle flange):

Assume a Knee brace at the end of the haunch;

Check width to thickness ratio for compression member

Table 3

Flange:

<

class 1 for compression flanges

>

Web of Rafter:

>

Web for Haunch:

Section is class 4 for compression web of the rafter and haunch

Check width to Thickness Ratio- for Flexural Compression Member

Table 4

Flange:

<

Section Class 2 for Flexural Compression flanges

Web of Rafter:

<

Section Class 1 for Flexural Compression for rafter web

Web of Hauch:

<

Section Class 3 for Flexural Compression for web of Haunch

Check Compression

Calculate the λ Factor

Buckling Length Factor;

Haunch Length with one Knee Brace at the end of the Haunch:

Check for Class 4 for Rafter

Stress f for rafter:

The web is supported by the flanges-Hence

For the Rafter:

<

Hence no Reduction in area is required for rafters

Check for Class 4 Haunch

Stress f for Hauch:

The web is supported by the flanges-Hence:

For Haunch

<

Hence Reduction in area is not required

As Precaution Check the Effective Area of the Haunch

Web Height Required is

Adopth the min of

Effective Area of Haunch:

Calculate λ:

The Factorised Axial Compression Resistance is:

Hot Rolled Steel Factor is:

Rafter Compression Resistance at Haunch End

>

Rafter Compression at Haunch Start

>

Check Bending - Class 4

Moment My at the Bottom of Haunch:

Calculate ω2

Factor ω2 see Galambos

< 2.5

K.h for bending :

Critical Moment at Hanch

>

Check Buckling Torsional Resistance:

>

Check Member Stability

Memeber subjected to UDL or series of PL

C. fh

Value CXe at start of Haunch:

Value Ux1:

Hauch Stability:

< 1 OK!

Check Moment of Resistance of Tension Flange:

Moment My at the top of the Haunch:

>

Check Rafter Between Eaves and Haunch and Apex Haunch

Max uplift Force

start node

Case 33

Beam 14

end node

Max downward Force

start node

Case 132

Beam 14

end node

NOTE - For Case 33 the Top Flange of the Rafter is in Compression The Top Flange is Torsionally Restrained by the Purlins. The Purlins also restrain the Rafter in the Y-Y direction, while in the X-X Direction the Rafter is Restrained by the Knee bracings placed at the end of the Haunches. For Case 25 the Bottom Flange is in compression and it is Restrained by the Knee Bracings Placed at the end on the Haunches. For this case the Rafter is in tension.

Due to the low forces in case 33 (uplift) the effect is negligible and will not be analysed

Check Case 132

Buckling Lengths:

Check Compression

Calculate Minimum λ:

The Factorised Axial Compression Resistance is:

Hot Rolled Factor:

Rafter Compression REsistance at Haunch end

>

Check For Torsional Moment

Moment My of the rafter:

>

Calculate M.cr

Assume ω2=1

Kh for bending:

Critical Moment at Rafter

>

The Buckling Torsional is:

>

Check member stability-

Check Member Stability

Value ω1:

member subjected to UDL or series of PL

Value C fh:

Value Cxe:

Value Ux.1:

Rafter Stability

< 1.0 Okay!

Check Apex Haunch

Forces at Apex:

Max uplift Force

start node

Case 33

Beam 65

end node

Max downward Force

start node

Case 132

Beam 14

end node

NOTE - For Case 26 the Top Flange of the Haunch is in Compression The Top Flange is Torsionally Restrained by the Purlins The Purlin also restrain the Rafter in the Y-Y direction, while in the X-X Direction the Rafter is Restrained by the Knee Bracings. For Case 27 the Bottom Flange is in compression and it is Restrained by the Knee Bracings. For this case the Rafter is in tension.

By Inspection the apex haunch is Okay

Column Design

Section of Column that occures singularly above the braced Section.

Load Case

Properties of 356x171x45 Column:

Depth of Column:

Width of Column:

Flange thickness:

Web thickness:

Radius at web:

Column Area:

Column moment of inertias:

Section Moduli of Column:

Radius of gyration of Column:

Plastic moduli:

Saint Venant Constant:

Warping Constant:

Check Width to thickness Ratio for compression member table 3 for Rafters and haunches

Flange:

<

Flange is class 1

Web of Column:

>

Check Width to thickness ratio for flexural compression member table 4 for rafter and haunch

Flange:

<

Web of Column:

<

Section Class 1 for Flexural Compression for Column Web

Buckling Length:

Check Compression:

Calculate minimum λ:

Hot rolled Factor:

>

Check for Torsional Moment

Moment My of the column

>

Calculate M.cr

Calculate ω2

< 2.5

K for bending:

Critical Moment at Column

>

The Buckling Torsional Resistance is:

>

Check Member Stability

Value ω1:

Value C fcl:

Value Ce:

Value U1:

Column Stability:

< 1 Okay!

Check Dual Column Section

Properties of 356x171x45 Column:

Depth of Column:

Width of Column:

Flange thickness:

Web thickness:

Depth of web:

Radius at web:

Column Area:

Column moment of inertias:

Section Moduli of Column:

Radius of gyration of Column:

Plastic moduli:

Saint Venant Constant:

Warping Constant:

Section Classification

Outstanding Compression Flange:

11.3.1.c

Limiting width to thickness ratio

Table 3

hence not slender

Web in Axial Compression

Limiting width to thickness ratio

Hence Cross section is class 4

Check Slenderness ratio

<200

Calculate f.e

Check For Torsional-Flexural buckling

>

Hence OK

By Inspection Both of the Columns are sufficient

60X60X6 L Bracing Check

Load Inputs:

Loads At ULS Limit state

Cross Section Information

Tension member Check

Note not the Connection resistance only the member resistance is considered due to available information

T.r is the leas of T.r_1 to 4

Section Classification

Outstanding leg

Compressive resistance check

Check Slenderness ratio

10.4.2.1

< 200

< 200

Recommended Design Value as ideal conditions are approximated

use goal seek to solve for the smallest root of the formula below with f.e being the variable

hence compressive resistance is:

Check With BS

According to red book table

60x60x6

Hence Red book is more conservative

60x60x8

>

hence OK!!

Short Channel beams

By Inspection is OK

Conncections

Plate Width:

Number of bolts per row:

Number of bott bolts:

Total depth of Haunch:

Distance from top of beam flange to 1st bolt:

Distance between top bolts:

Distance from bott of haunch to bott bolt:

Thickness end plate:

Check Load case 132 node 20

Load Case

Actual Moment taking the axial force into account:

Lever arm to centre of bottom flange 1st bolt row:

Lever arm to centre of bottom flange 2nd bolt row:

Max 1st Row Bolt Tension:

per bolt

Max 2st Row Bolt Tension:

per bolt

Total Tension of the group:

Max Bolt Shear

(Bottom Bolts only):

Sizing of bolt rule of thumb:

bolt area:

Adopt M20 Bolts GR.8.8

Bolt Diameter:

Bolt hole Diameter:

Area of bolt:

Tension Capacity:

>

hence OK!

Shear Capacity:

>

hence OK!

Note:

1-The tension capacity is calculated with the bolt net area and does not include any prying action.

2-The shear capacity is calculated with the bolt net area.

Combined Tension and Shear is not yet applicable.

End Plate Welding:

Weld Ultimate Strength:

Parent metal yield Stress:

Material Factor:

Design Strength for Von Mises Check:

1st Iteration try:

Flange Welds:

Throat:

Web Welds:

Throat:

Calculate welds moment of inertia:

Weld Length to top of Flange:

Weld Length to bottom of Flange:

Weld Length to web

Distance of welds to top of flange to centre of haunch:

Welds moment of inertia:

Weld section modulus for flange weld:

Weld section modulus for web weld:

Area of web welds resisting shear:

Check Welds to Web

Web weld shear stress(along weld):

<

Web weld bending stress:

<

Weld Combined Stress:

Weld stress pattern to web

Shear causes a stress along the weld which is caled t.paral

<

Hence the welds to web are O.K for Shear and for combined stress

Check Welds to Flange

Max. Flange weld Bending Stress:

<

Weld stress pattern to flange

Then welds to flanges are Okay-

ADOPT 10mm Fillet Weld to Flanges and 8 mm F.W to Web

End Plate Design:

Plate Size:750 x 171

Max plate thickness is

Note: The Check is carried out using the BSCA-Green BOOK Joint in steel Construction- moment connections-

Rigorous Analysis

Potential resistance of bolts in the tension zone.

Adopt 14mm thk Plate

Adopt Plate thickness:

For flange weld:

For web fillet weld:

Check End Plate and Column Flange Plastic Distribution Limit

Check end Plastic Limit:

Check Column Flange Plastic Limit:

Hence OK.

Note: According to Step 1C p25 Paragraph below Figure2.18,<< The Triangular Distribution only needs to be imposed if Both Sides of the connection exceed their respective Thickness Limits>>

Check Haunch Connection

From Table 2.6- Bolt Row of a Group Below Beam Flange of a Flush End Plate.

From Table 2.1 - Tensile Capacity of a Single M30-8.8 Bolts in accordance to the Green Book

<

Rafter 356 x 171 x 45 UB

Rafter Flange Width:

Rafter Web thickness:

Rafter Flange Thickness:

Rafter Web Radius:

Column 356 x 171 x 45 UB

Column Flange Width:

Column Web thickness:

Column Flange thickness:

Column Web Radius:

End Plate and Column Flange

Plate Width:

End Plate Thickness:

Column Flange Thickness:

Bolt edge distance:

Distance from bolt lines -

B.cap>=g.b:

Vertical distance between bolts:

Cap Plate Thickness must be >=0.8 x t.pl

Distance to edge of plate:

Distance from top bolt of cap plate:

Distance m1 for end plate:

Distance m2 for end plate:

Distance m1 for column:

Distance m2 for column:

Bolts in Row 1

Column Flange bending-the bolt row 1 is influenced by the cap plate.

From tabel 2.5-bolt row next to a cap plate-

since:

<

and

>

Use Min(Max[(ii,iii),i)

Pattern i:

Pattern ii:

Pattern iii-Calculte α

From Figure 2.16

Pattern iii)

Check Column Flange

End plate Plastic Moment:

Check Mode 1 - Complete Plate Yielding

Resisting Force:

Check Mode - Bolt Failure with Plate Yielding

Resisting Force:

Check Mode 3- Bolt Failure

Resisting Force:

Minimum Flange Resisting Force -Row 1:

Check Column Web in Tension-Step 1B Page 24

Web Resisting tension (one bolt):

End Plate Bending - The Bolt Row 1 is influenced by the Beam Flange

since:

<

and

=

From Table 2.5 bolt row below beam flange of a flush end plate

Pattern i:

Pattern ii:

Pattern iii - Calculate α

The plate effective lengths:

Check End Plate

End plate plastic Moment:

Check mode 1-Complete plate yielding:

Resisting Force:

Check mode 2-Bolt failure with plate yielding:

Resisting force:

Check mode 3-Bolt failure

Resisting Force:

Minimum End plate Resting force for row 1:

Note: The triangular limit do not apply to Row 1 - Hence the minimum resistance is given by:

Potential Resistance Pr1 for row 1

Bolts in Row 2

Column Flange Bending The bolts Row 2 are not influenced by the beam flange

From Table 2.5-bolt row of a group next to a column cap plate -

Use Min(ii,iii)

Pattern i:

Pattern ii:

Hence plate effective length:

End plate plastic moment:

Check Mode 1- complete plate yielding

Resisting Force:

Check Mode 2- Bolt Failure with Plate yielding:

Resisting Force:

Check Mode 3- Bolt Failure

Resisting Force:

Minimum Flange Resting Force Row 2:

Check Column Web in Tension- Step 1B p24

Web Resisting tension (one bolt):

End Plate Bending - The Bolt Row 2 is not influenced by the beam flange

From table 2.5 Bolt Row not influenced by a stiffenert or free edge

Use Min(ii,ii)

Pattern i:

Pattern ii:

The plate effective lengths:

Check End Plate

End Plate Plastic Moment:

Check Mode 1- complete plate yielding

Resisting Force:

Check Mode 2- Bolt Failure with Plate yielding:

Resisting Force:

Check Mode 3- Bolt Failure

Resisting Force:

Therefore the Row yw is taken as the minimum from mode 1 to 3 - Pr1

Minimum Flange Resting Force Row 2:

Potential Resistance Pr2 for Row 2:

Bolts in Row 1 & 2 Combined

Column Flange Bending - The top bolts of row 1 is influenced by the cap plate where the bolts in row 2 are not influenced by the cap plate.

Since:

<

&