STRUCTURAL CALCULATIONS FOR REAR EXTENSION AND LOFT … … · New Lintel L2 is to be 1No. 1950mm...

Structural Calculations for Double Storey Rear Extension and Loft Conversion

Samir PatelDW 06/05/2018 A

Ruthin Road Blackheath

SE3 7SH

CALCULATION SHEET

PROJECT

CALCULATIONS FOR

ORIGINATOR DATE PAGE REVISION

00

This calculation pack contains the following:

Beam and Roof Layout PlansLintel Calculation Beams Calculation Connection DetailsTimber DesignStrip Footing Design Structural design notes

(Pages 01 - 02)(Pages 03 - 11)(Pages 12 - 29)(Pages 30 - 35)(Pages 36 - 42)(Pages 43 - 44)(Pages 45)

STRUCTURAL CALCULATIONS FOR DOUBLE STOREYREAR EXTENSION AND LOFT CONVERSION

New Lintel L1 is to be 1No. 3150mm Catnic LintelNew Lintel L2 is to be 1No. 1950mm Catnic LintelNew Lintel L3 is to be 1No. 2250mm Catnic LintelNew Beam B1 is to be 1No. 152x152x30 UBNew Beam B2 is to be 1No. 152x152x30 UBNew Beam B3 is to be 1No. 254x254x73 UBNew Beam B4 is to be 1No. 254x254x73 UB Extension Floor Joists are to be 47x175 C24 Timbers at Max. 400mm centres

Loft Floor Joists are to be 47x200 C24 Timbers at Max. 200mm centresLoft Floor Joists are to be 47x175 C24 Timbers at Max. 600mm centresNew Strip Footing is to be 500x400 Unreinforced Concrete

Executive Summary

2

Lintel Calculation

Lintel L1

LINTEL ANALYSIS

In accordance with BS5977-1:1981 incorporating Amendment No. 1 Tedds calculation version 1.1.00

Masonry

2750

302527

00

Basic lintel dimensions;Lintel clear span; Lc1 = 2750 mm

Lintel load application length; L = Lc1 1.1 = 3025 mm

Load zone height; hLZ = tan(45) L / 2 = 1513 mm

Interaction zone height; hIZ = tan(60) L / 2 = 2620 mm

Load factorsDead load factor; LFd = 1.40Imposed load factor; LFI = 1.60

MasonryMasonry height; hm = 2700 mm

Leaf 1;

Masonry density; mi = 20.00 kN/m3

Masonry thickness; twi = 100 mm

Load at midspan; wmi = hLZ twi mi = 3.025 kN/m

Cavity width; tcav = 100 mm

Leaf 2;

Masonry density; mo = 20.00 kN/m3

Masonry thickness; two = 100 mm

Load at midspan; wmo = hLZ two mo = 3.025 kN/m

Lintel Calculation

Lintel L1

Lintel self weightSelf weight of lintel; wlsw = 1.000 kN/m

Masonry load zoneHeight of load zone; hLZ = L / 2 = 1513 mm

Total masonry area; ALZ = hLZ L / 2 = 2.288 m2

Total masonry load; WLZ = ALZ (two mo + twi mi) = 9.151 kN

Equivalent UDL; wEquiv_LZ = WLZ 1.33 / L = 4.023 kN/m

Load application summary;

Load DescriptionUDL total

length(mm)

Start of UDLon lintel

(mm)

End of UDLon lintel

(mm)

Equiv.dead loadon lintel(kN/m)

Equiv.imposed load

on lintel(kN/m)

Masonry from load triangle 3025 0 3025 4.023 0.000

Analysis results at ULSMaximum moment; Mmax = 8.060 kNm

Maximum shear; Vmax = 8.523 kN

Maximum reaction at support A; RA_max = 8.523 kN

Maximum reaction at support B; RB_max = 8.523 kN

Support reactions at SLSDead loads

Reaction at support A; RA_DL = 6.088 kN

Reaction at support B; RB_DL = 6.088 kN

Imposed loads

Reaction at support A; RA_IL = 0.000 kN

Reaction at support B; RB_IL = 0.000 kN

Equivalent UDL at SLSTotal equivalent UDL (inc. selfweight); we = 5.023 kN/m

8.1

0

Moment

Lintel Calculation

Lintel L1

8.5

-8.5

Shear

Choosen Catnic lintel size: 3150 mm

Lintel Calculation

Lintel L2

LINTEL ANALYSIS


Masonry

1728

1901

270

0







Leaf 1;





Leaf 2;




Lintel Calculation

Lintel L2








length(mm)


(mm)

End of UDLon lintel

(mm)


Equiv.imposed load

on lintel(kN/m)









Imposed loads




2.2

0

Moment

Lintel Calculation

Lintel L2

3.9

-3.9

Shear


Lintel Calculation

Lintel L3

LINTEL ANALYSIS


Masonry

2010

2211

27

00







Leaf 1;





Leaf 2;




Lintel Calculation

Lintel L3








length(mm)


(mm)

End of UDLon lintel

(mm)


Equiv.imposed load

on lintel(kN/m)









Imposed loads




3.4

0

Moment

Lintel Calculation

Lintel L3

5

-5

Shear


Load Calculation

Beam B1

Item Unfactored Load (KN/m2) Load Type GK/QK Factored Load (KN/m

2)

Floor joists 0.3 Dead 1.4 0.42

Chipboard 0.15 Dead 1.4 0.21

Timber Floorboards 0.16 Dead 1.4 0.224

Plasterboard 0.12 Dead 1.4 0.168

Insulation 0.03 Dead 1.4 0.042

Residential Live Loading 2 Live 1.6 3.2

Total 4.27 (KN/m2)

Table 1.1 ‐ Internal Floor Loads

Item Span (m) Load (KN/m2) Comments UDL Load (KN/m)

First Floor Loading 2 4.27 See Load Table 1.1 8.54

Total 8.54 (KN/m)

Table 1.2 ‐ Proposed UDLs

Beams Calculations

Beam B1

STEEL BEAM ANALYSIS & DESIGN (BS5950)

In accordance with BS5950-1:2000 incorporating Corrigendum No.1TEDDS calculation version 3.0.05

Load Envelope - Combination 1

0.0

8.835

mm 41501A B

Bending Moment Envelope

0.0

19.019

kNm

mm 41501A B

19.0

Shear Force Envelope

0.0

18.332

-18.332

kN

mm 41501A B

18.3

-18.3

Support conditionsSupport A Vertically restrained

Rotationally free

Support B Vertically restrained

Rotationally free

Applied loadingBeam loads Dead self weight of beam 1

Dead full UDL 8.54 kN/m

Load combinationsLoad combination 1 Support A Dead 1.00

Imposed 1.00

Span 1 Dead 1.00

Imposed 1.00

Support B Dead 1.00

Imposed 1.00

Beams Calculations

Beam B1

Analysis resultsMaximum moment; Mmax = 19 kNm; Mmin = 0 kNm

Maximum shear; Vmax = 18.3 kN; Vmin = -18.3 kN

Deflection; max = 9.5 mm; min = 0 mm

Maximum reaction at support A; RA_max = 18.3 kN; RA_min = 18.3 kN

Unfactored dead load reaction at support A; RA_Dead = 18.3 kN

Maximum reaction at support B; RB_max = 18.3 kN; RB_min = 18.3 kN

Unfactored dead load reaction at support B; RB_Dead = 18.3 kN

Section detailsSection type; UC 152x152x30 (BS4-1)Steel grade; S275

From table 9: Design strength py

Thickness of element; max(T, t) = 9.4 mm

Design strength; py = 275 N/mm2

Modulus of elasticity; E = 205000 N/mm2

152.9

6.5

15

7.6

9.4

9.4

Lateral restraintSpan 1 has lateral restraint at supports only

Effective length factorsEffective length factor in major axis; Kx = 1.00Effective length factor in minor axis; Ky = 1.00

Effective length factor for lateral-torsional buckling; KLT.A = 1.00; + 2 D

KLT.B = 1.00;

Classification of cross sections - Section 3.5 = [275 N/mm2 / py] = 1.00

Internal compression parts - Table 11Depth of section; d = 123.6 mm

d / t = 19.0 <= 80 ; Class 1 plastic

Beams Calculations

Beam B1

Outstand flanges - Table 11Width of section; b = B / 2 = 76.5 mm

b / T = 8.1 <= 9 ; Class 1 plastic

Section is class 1 plastic

Shear capacity - Section 4.2.3Design shear force; Fv = max(abs(Vmax), abs(Vmin)) = 18.3 kN

d / t < 70 Web does not need to be checked for shear buckling

Shear area; Av = t D = 1024 mm2

Design shear resistance; Pv = 0.6 py Av = 169 kN

PASS - Design shear resistance exceeds design shear force

Moment capacity - Section 4.2.5Design bending moment; M = max(abs(Ms1_max), abs(Ms1_min)) = 19 kNm

Moment capacity low shear - cl.4.2.5.2; Mc = min(py Sxx, 1.2 py Zxx) = 68.1 kNm

Effective length for lateral-torsional buckling - Section 4.3.5Effective length for lateral torsional buckling; LE = ((1.0 + 1.0) Ls1 + 2 D) / 2 = 4308 mm

Slenderness ratio; = LE / ryy = 112.552

Equivalent slenderness - Section 4.3.6.7Buckling parameter; u = 0.849Torsional index; x = 15.999

Slenderness factor; v = 1 / [1 + 0.05 ( / x)2]0.25 = 0.732

Ratio - cl.4.3.6.9; W = 1.000

Equivalent slenderness - cl.4.3.6.7; LT = u v [W] = 69.950

Limiting slenderness - Annex B.2.2; L0 = 0.4 (2 E / py)0.5 = 34.310

LT > L0 - Allowance should be made for lateral-torsional buckling

Bending strength - Section 4.3.6.5Robertson constant; LT = 7.0

Perry factor; LT = max(LT (LT - L0) / 1000, 0) = 0.249

Euler stress; pE = 2 E / LT2 = 413.5 N/mm2

LT = (py + (LT + 1) pE) / 2 = 395.8 N/mm2

Bending strength - Annex B.2.1; pb = pE py / (LT + (LT2 - pE py)0.5) = 188.5 N/mm2

Equivalent uniform moment factor - Section 4.3.6.6Moment at quarter point of segment; M2 = 14.3 kNm

Moment at centre-line of segment; M3 = 19 kNm

Moment at three quarter point of segment; M4 = 14.3 kNm

Maximum moment in segment; Mabs = 19 kNm

Maximum moment governing buckling resistance; MLT = Mabs = 19 kNm

Equivalent uniform moment factor for lateral-torsional buckling;

mLT = max(0.2 + (0.15 M2 + 0.5 M3 + 0.15 M4) / Mabs, 0.44) = 0.925

Beams Calculations

Beam B1

Buckling resistance moment - Section 4.3.6.4Buckling resistance moment; Mb = pb Sxx = 46.7 kNm

Mb / mLT = 50.5 kNm

PASS - Buckling resistance moment exceeds design bending moment

Check vertical deflection - Section 2.5.2Consider deflection due to dead and imposed loads

Limiting deflection;; lim = Ls1 / 360 = 11.528 mm

Maximum deflection span 1; = max(abs(max), abs(min)) = 9.522 mm

PASS - Maximum deflection does not exceed deflection limit

Structural calculations for padstones

Beam B1

Beam End Reaction = 18.4 KN (factored) Variable Load Safety Factor = 1.5

Permanent Load Safety Factor = 1.35

Characteristic strength of masonry = 2.8 N/mm2 (Brickwork Usually = 4.5 N/mm2)

(3.6N Blockwork usually = 2.6 N/mm2)

Width of beam end bearing = 153 mm (A Engineering Brick = 13.2 N/mm2)

Length of beam end bearing = 100 mm (B Engineering Brick = 10.5 N/mm2)

(Weak Brickwork = approx 2.8 N/mm2)



ᵧm = 3

Bearing Factor = 1.25

Results

Maximum Bearing Stress = 1.17 N/mm2

Actual Bearing Stress = 1.2 N/mm2

Padstone Results

Characteristic strength of padstone = 30 N/mm2

Width of Padstone = 100 mm

Length of Padstone = 200 mm

Allowable padstone stress = 12.5 N/mm2

Stress under beam end bearing = 1.2 N/mm2 Therefore Padstone Stress OK

Allowable masonry stress = 1.17 N/mm2

Stress under padstone = 0.92 N/mm2 Therefore Masonry Stress OK

Padstone Required for Loads Applied

Load Calculation

2Beam B


Dormer Walls 2.6 1 1 KN/m2 assumed for mber construc on 2.6

Wall ( Span is effective height of wall

loading beam )5.5 4.74

External walls‐ 302.5mm thick; 102.5mm

outer brick skin, 150mm blockwork skin,

plaster finish

26.07

Beam B1 Reac on ‐ ‐ KN @ 1830mm

Total 28.67 (KN/m)


18.3

Beams Calculations

Beam B2




0.0

28.965

mm 26001A B


0.0

32.028

kNm

mm 26001A B

32.0 30.3


0.0

43.074

-50.534

kN

mm 26001A B

43.1

-9.9

-50.5


Rotationally free


Rotationally free



Dead point load 18.3 kN at 1830 mm


Imposed 1.00

Span 1 Dead 1.00

Imposed 1.00

Support B Dead 1.00

Beams Calculations

Beam B2

Imposed 1.00

Analysis resultsMaximum moment; Mmax = 32 kNm; Mmin = 0 kNm












152.9

6.5

15

7.6

9.4

9.4




KLT.B = 1.00;



d / t = 19.0 <= 80 ; Class 1 plastic

Beams Calculations

Beam B2







Design shear resistance; Pv = 0.6 py Av = 169 kN


Moment capacity - Section 4.2.5Design bending moment; M = max(abs(Ms1_max), abs(Ms1_min)) = 32 kNm






Ratio - cl.4.3.6.9; W = 1.000







LT = (py + (LT + 1) pE) / 2 = 567.3 N/mm2

Bending strength - Annex B.2.1; pb = pE py / (LT + (LT2 - pE py)0.5) = 234.7 N/mm2


Moment at centre-line of segment; M3 = 31.5 kNm


Maximum moment in segment; Mabs = 32 kNm

Maximum moment governing buckling resistance; MLT = Mabs = 32 kNm


mLT = max(0.2 + (0.15 M2 + 0.5 M3 + 0.15 M4) / Mabs, 0.44) = 0.920

Beams Calculations

Beam B2


Mb / mLT = 63.2 kNm







2Beam B

Beam End Reaction = 51 KN (factored) Variable Load Safety Factor = 1.5









ᵧm = 3


Results



Padstone Results









Load Calculation

3 & B4s BBeam


2)







Total 4.27 (KN/m2)



Loft Floor Loading 2 4.27 See Load Table 4.1 8.54

Dormer Walls 5.8 1 1 KN/m2 assumed for mber construc on 5.8

Total 14.34 (KN/m)


Beams Calculations

Beams B3 & B4




0.0

15.057

mm 58001A B


0.0

68.898

kNm

mm 58001A B

62.968.9


0.0

47.579

-45.549

kN

mm 58001A B

47.6

19.2

-45.5


Rotationally free


Rotationally free



Dead point load 5.8 kN at 1885 mm


Imposed 1.00

Span 1 Dead 1.00

Imposed 1.00

Support B Dead 1.00

Beams Calculations

Beams B3 & B4

Imposed 1.00

Analysis resultsMaximum moment; Mmax = 68.9 kNm; Mmin = 0 kNm












254.6

8.6

254

.1

14

.21

4.2




KLT.B = 1.00;



d / t = 23.3 <= 80 ; Class 1 plastic

Beams Calculations

Beams B3 & B4







Design shear resistance; Pv = 0.6 py Av = 360.6 kN


Moment capacity - Section 4.2.5Design bending moment; M = max(abs(Ms1_max), abs(Ms1_min)) = 68.9 kNm






Ratio - cl.4.3.6.9; W = 1.000







LT = (py + (LT + 1) pE) / 2 = 441.3 N/mm2

Bending strength - Annex B.2.1; pb = pE py / (LT + (LT2 - pE py)0.5) = 205 N/mm2


Moment at centre-line of segment; M3 = 68.8 kNm


Maximum moment in segment; Mabs = 68.9 kNm

Maximum moment governing buckling resistance; MLT = Mabs = 68.9 kNm


mLT = max(0.2 + (0.15 M2 + 0.5 M3 + 0.15 M4) / Mabs, 0.44) = 0.924

Beams Calculations

Beams B3 & B4


Mb / mLT = 220.1 kNm







s B3 & B4Beam

Beam End Reaction = 46 KN (factored) Variable Load Safety Factor = 1.5









ᵧm = 3


Results



Padstone Results









Connection Details

SC1

;BEAM TO BEAM - CLEAT CONNECTION TEDDS calculation version 2.0.16

Section Details

Supporting Beam - UC 152x152x30;; Gradesupporting = "S275"

Supported Beam - UC 152x152x30;; Gradesupported = "S275"

Cleats 2 x RSA 70x70x10;; Gradecleats = "S275"

Bolts M12 (Grade 8.8)

A

A

SECTION THROUGH SUPPORTING BEAM

30

10

0

10 Gap

SECTION A - A

30

Connection Details ; Bolt eccentricity for supported beam; abolts = 50 mm

; number of bolt rows; nbolts = 3

; Bolt pitch;; pbolts = 30 mm

; Bolt gauge; gbolts = 107 mm

; End projection; t1 = 10 mm

; Cleat end distance (top & bottom); e1cleats = 20 mm

; Cleat edge distance on supported beam; e2cleatssupported = 20 mm

; Cleat edge distance on supporting beam; e2cleatssupporting = 20 mm

Cleat length; lcleats = pbolts(nbolts-1)+2e1cleats = 100 mm

;Supported Beam end reaction; Q = 18.5 kN

Notch details; Top notch length; ctopnotch = 83 mm

; Top notch depth; dctopnotch = 20 mm

; Bottom notch length; cbottomnotch = 83 mm

; Bottom notch depth; dcbottomnotch = 20 mm

Check 1 - Essential detailing requirements

; Cleat thickness; tcleats = 10 mm; PASS

; Bolt gauge; gbolts = 107 mm; PASS

; Cleat Length; lcleats = 100 mm

; Cleat length for torsional requirements : PASS; ; Cleats fit between beam fillets : PASS

Check 2 - Shear capacity of bolt group connecting cleats to web of supported beam (taking account of eccentricity 'a') ;;;; Elastic section modulus of bolt group

Zbolts = nbolts (nbolts + 1) pbolts / 6 = 60 mm

Force on outermost bolt due to moment

Fm = Q abolts / Zbolts = 15 kN

Connection Details

SC1

Force on bolt due to shear

Fv = Q / nbolts = 6.2 kN

Resultant force on bolt due to direct shear and moment

Fr = (Fv2 + Fm

2)= 16.6 kN

Shear capacity of a single bolt in double shear

;2 Psbolts = 63.2 kN

Utilisation factor; Ucheck2shear = Fr / (2 Psbolts) = 0.263

Shear capacity to web : PASS

Check 3 - Shear and bearing capacity of cleat connected to supported beam

for shear

;;

pycleats = 275 N/mm2

;; e1acleats = e1cleats = 20 mm

;; Avcleats = 0.9 (2 e1acleats + (nbolts - 1) pbolts) tcleats = 900 mm2

; Avnetcleats = Avcleats - nbolts Dhbolts tcleats = 480 mm2

Effective net area coefficient

Kecleats = 1.20

Plain shear capacity of cleats

PvPcleats = min(0.6 pycleats Avcleats, 0.7 Kecleats pycleats Avnetcleats) = 110.9 kN

Av1cleats = (e1acleats + (nbolts - 1) pbolts) tcleats = 800 mm2

; Ateffcleats = (e2cleatssupported - 0.5 Dhbolts) tcleats = 130 mm2

PvBcleats = 0.6 pycleats Av1cleats + 0.6 Kecleats pycleats Ateffcleats = 157.7 kN

Shear capacity of the angle cleat leg; Pvcleats = min (PvPcleats, PvBcleats) = 110.9 kN

;Shear force on angle cleat; Q / 2 = 9.3 kN

Utilisation factor; Ucheck3shear = Q / (2 Pvcleats) = 0.083

Shear capacity of cleats to beam: PASS

for bearing

ecleats = min (e1cleats, e2cleatssupported) = 20 mm

bearing strength of the cleat

pbscleats = 460 N/mm2

bearing capacity of the leg of the angle cleat per bolt

Pbscleats = min(dbolts tcleats pbscleats, 0.5 ecleats tcleats pbscleats) = 46.0 kN

;Bearing force on cleat; Fr / 2 = 8.3 kN

Utilisation factor; Ucheck3bearing = Fr / (2 Pbscleats) = 0.180

Bearing capacity of cleats to beam: PASS

Check 4b - shear and bearing capacity of the supported beam (2 notches)

;;;;for shear

;;

pysupported = 275 N/mm2

Connection Details

SC1

; Distance top supported beam to 1st hole; etsupported = 50 mm

;;; etasupported = etsupported - dctopnotch = 30 mm

; ebsupported = Dsupported - etsupported - (nbolts - 1) pbolts = 48 mm

ebasupported = ebsupported - dcbottomnotch = 28 mm

; Avsupported = 0.9 (etasupported + (nbolts - 1) pbolts + ebasupported) tsupported = 688 mm2

; Avnetsupported = Avsupported - nbolts Dhbolts tsupported = 415 mm2


Kesupported = 1.20

Plain shear capacity of beam

PvPsupported = min(0.6 pysupported Avsupported, 0.7 Kesupported pysupported Avnetsupported) = 95.9 kN

Av1supported = (etasupported + (nbolts - 1) pbolts) tsupported = 585 mm2

;; e3supported = abolts - t1 = 40 mm

Ateffsupported = (e3supported - 0.5 Dhbolts) tsupported = 215 mm2

Block shear capacity of beam

PvBsupported = 0.6 pysupported Av1supported + 0.6 Kesupported pysupported Ateffsupported = 139.0 kN

Shear capacity of the beam; Pvsupported = min (PvPsupported, PvBsupported) = 95.9 kN

;Shear force on beam; Q = 18.5 kN

Utilisation factor; Ucheck4shear = Q / Pvsupported = 0.193

Shear capacity of beam : PASS

for bearing

bearing strength of the beam

pbssupported = 460 N/mm2

bearing capacity of the beam per bolt

Pbssupported = min(dbolts tsupported pbssupported, 0.5 e3supported tsupported pbssupported) = 36 kN

;Resultant bearing force on bolts; Fr = 16.6 kN

Utilisation factor; Ucheck4bearing = Fr / Pbssupported = 0.463

Bearing capacity of beam : PASS

Check 4c - bending capacity of reduced beam section at the notch - 2 flanges notched ;;;;;; Znotched = tsupported (Dsupported - dctopnotch - dcbottomnotch)2 / 6 = 14982 mm3

;Moment capacity of notched section; Mcapnotched = pysupported Znotched = 4.1 kNm

;Moment applied to notched section; Mappnotched = Q max(ctopnotch, cbottomnotch) = 1.5 kNm

Utilisation factor; Ucheck4cmoment = Mappnotched / Mcapnotched = 0.374

Moment capacity of notched section : PASS

Check 4d - local stability of notched beams restrained against lateral torsional buckling - 2 flanges notched

;;;; Depth of top notch; dctopnotch = 20 mm

Length of top notch; ctopnotch = 83 mm

Depth of bottom notch; dcbottomnotch = 20 mm

Length of bottom notch; cbottomnotch = 83 mm

Connection Details

SC1

Checkdepth = max(dctopnotch, dcbottomnotch) = 20 mm

Checklength = max(ctopnotch, cbottomnotch) = 83 mm

;Depth of both notches less than limit of D/5 : PASS

; Gradesupported = "S275"

;; dot = Dsupported/tsupported = 24.2

climit = if(or(Gradesupported == “S275”, Gradesupported == “300”), if(dot<=54.3,Dsupported,160000 Dsupported/dot3),

if(dot<=48.0,Dsupported,110000 Dsupported/dot3))

climit = 157.6 mm

Length of both notches less than limit : PASS

Check 5 - Shear capacity of bolt group connecting cleats to supporting beam

Shear capacity of top pair of bolts

;;;;; Psbolts1 = min(Psbolts, 0.5 e1cleats tcleats pbscleats) = 31.6 kN

Shear capacity of other bolts

Psbolts = 31.6 kN

Shear capacity of bolt group - sum of bolt capacities

;Psboltssum = 2 Psbolts1 + 2 (nbolts - 1) Psbolts = 189.7 kN

;Shear on bolt group; Q = 18.5 kN

Utilisation factor; Ucheck5 = Q / Psboltssum = 0.098

Shear capacity of bolt group to supporting beam : PASS

Check 6 - Shear and bearing capacity of cleats connected to supporting beam

for shear

;;

pycleats = 275 N/mm2

;; e1acleats = e1cleats = 20 mm

;; Avcleats = 0.9 (2 e1acleats + (nbolts - 1) pbolts) tcleats = 900 mm2


Kecleats = 1.20

; Avnetcleats = Avcleats - nbolts Dhbolts tcleats = 480 mm2

Plain shear capacity of cleats

PvPcleats = min(0.6 pycleats Avcleats, 0.7 Kecleats pycleats Avnetcleats) = 110.9 kN

Av1cleats = (e1acleats + (nbolts - 1) pbolts) tcleats = 800 mm2

; Ateffcleatssupporting = (e2cleatssupporting - 0.5 Dhbolts) tcleats = 130 mm2

Block shear capacity of cleats

PvBcleatssupporting = 0.6 pycleats Av1cleats + 0.6 Kecleats pycleats Ateffcleatssupporting = 157.7 kN

Shear capacity of the angle cleat leg; Pvcleatssupporting = min (PvPcleats, PvBcleatssupporting) = 110.9 kN

;Shear force on angle cleat; Q / 2 = 9.3 kN

Utilisation factor; Ucheck6shear = Q / (2 Pvcleatssupporting) = 0.083

Shear capacity of cleats to supporting beam: PASS

Connection Details

SC1

for bearing

ecleatssupporting = e1cleats = 20 mm

bearing strength of the cleat

pbscleats = 460 N/mm2

For top bolt,


Pbscleatssupporting1 = min(dbolts tcleats pbscleats, 0.5 ecleatssupporting tcleats pbscleats) = 46.0 kN

For other bolts,


Pbscleatssupporting = dbolts tcleats pbscleats = 55.2 kN

Capacity of bolt group;

Pbscleatssupportingsum = 2 Pbscleatssupporting1 + 2 (nbolts - 1) Pbscleatssupporting = 312.8 kN

Bearing force on bolt group; Q = 18.5 kN

Utilisation factor; Ucheck6bearing = Q / Pbscleatssupportingsum = 0.059

Bearing capacity of cleats to supporting beam: PASS

Check 7 - Local shear and bearing capacity of supporting beam web

for shear;;;;;

;ebsupporting = min(pbolts, Dsupporting - etsupporting - (nbolts - 1) pbolts) = 30 mm

Avsupporting = (ebsupporting + (nbolts - 1) pbolts + etsupporting) tsupporting = 910 mm2

; Avnetsupporting = Avsupporting - nbolts Dhbolts tsupporting = 637 mm2

;

pysupporting = 275 N/mm2


Kesupporting = 1.20

Pvsupporting = min(0.6 pysupporting Avsupporting, 0.7 Kesupporting pysupporting Avnetsupporting) = 147.1 kN

;Shear load on supporting beam; Q / 2 = 9.3 kN

Utilisation factor; Ucheck7shear = Q / (2 Pvsupporting) = 0.063

Local shear capacity of supporting beam web: PASS

for bearing

pbssupporting = 460 N/mm2

Pbssupporting = dbolts tsupporting pbssupporting = 35.9 kN

Q / (2 nbolts) = 3.1 kN

Utilisation factor; Ucheck7bearing = Q / (2 nbolts Pbssupporting) = 0.086

Local bearing capacity of supporting beam web : PASS

SUMMARY OF RESULTS

Check 2 - Capacity of bolt group connecting cleats to web of supported beam (taking account of eccentricity 'a')

Shear utilisation factor; Ucheck2shear = 0.263; PASS

Check 3 - Capacity of cleat connected to supported beam

Connection Details

SC1

Shear utilisation factor; Ucheck3shear = 0.083; PASS

Bearing utilisation factor; Ucheck3bearing = 0.180; PASS

Check 4b - Capacity of the supported beam Shear utilisation factor; Ucheck4shear = 0.193; PASSBearing utilisation factor; Ucheck4bearing = 0.463; PASS

Check 4c - bending capacity of reduced beam section at the notch - 2 flanges notched Moment Utilisation factor; Ucheck4cmoment = 0.374; PASS

Check 4d - local stability of notched beams restrained against lateral torsional buckling - 2 flanges notched Local stability limit; climit = 157.6 mm; PASS

Check 5 - Capacity of bolt group connecting cleats to supporting beam

Shear utilisation factor; Ucheck5 = 0.098; PASSCheck 6 - Capacity of cleats connected to supporting beam

Shear utilisation factor; Ucheck6shear = 0.083; PASSBearing utilisation factor; Ucheck6bearing = 0.059; PASS

Check 7 - Local capacity of column webShear utilisation factor; Ucheck7shear = 0.063; PASSBearing utilisation factor; Ucheck7bearing = 0.086; PASS

;

Floor Joists

Floor Extension & Dormer stFloor Joist Sizing for 1


2)







Total (Dead) 1.07 (KN/m2)

Total (Live) 3.2 (KN/m2)

Total 4.27 (KN/m2)


1st Floor Extension

1st Floor Extension- Span 3.00m

TIMBER JOIST DESIGN (BS5268-2:2002)Tedds calculation version 1.1.04

Joist detailsJoist breadth; b = 47 mm

Joist depth; h = 175 mm

Joist spacing; s = 400 mm

Timber strength class; C24Service class of timber; 1

mm 30001A B

Span detailsNumber of spans; Nspan = 1Length of bearing; Lb = 50 mm

Effective length of span; Ls1 = 3000 mm

175

47

50

Section propertiesSecond moment of area; I = b h3 / 12 = 20990885 mm4

Section modulus; Z = b h2 / 6 = 239896 mm3

Loading detailsJoist self weight; Fswt = b h char gacc = 0.03 kN/m

Dead load; Fd_udl = 1.07 kN/m2

Imposed UDL(Long term); Fi_udl = 3.20 kN/m2

Modification factorsService class for bending parallel to grain; K2m = 1.00

1st Floor Extension

1st Floor Extension- Span 3.00m

Service class for compression; K2c = 1.00Service class for shear parallel to grain; K2s = 1.00Service class for modulus of elasticity; K2e = 1.00Section depth factor; K7 = 1.06

Load sharing factor; K8 = 1.10

Consider long term loadsLoad duration factor; K3 = 1.00Maximum bending moment; M = 1.953 kNm

Maximum shear force; V = 2.604 kN

Maximum support reaction; R = 2.604 kN

Maximum deflection; = 8.500 mm

Check bending stressBending stress; m = 7.500 N/mm2

Permissible bending stress; m_adm = m K2m K3 K7 K8 = 8.754 N/mm2

Applied bending stress; m_max = M / Z = 8.142 N/mm2

PASS - Applied bending stress within permissible limits

Check shear stressShear stress; = 0.710 N/mm2

Permissible shear stress; adm = K2s K3 K8 = 0.781 N/mm2

Applied shear stress; max = 3 V / (2 b h) = 0.475 N/mm2

PASS - Applied shear stress within permissible limits

Check bearing stressCompression perpendicular to grain (no wane);cp1 = 2.400 N/mm2

Permissible bearing stress; c_adm = cp1 K2c K3 K8 = 2.640 N/mm2

Applied bearing stress; c_max = R / (b Lb) = 1.108 N/mm2

PASS - Applied bearing stress within permissible limits

Check deflectionPermissible deflection; adm = min(Ls1 0.003, 14 mm) = 9.000 mm

Bending deflection (based on Emean); bending = 8.077 mm

Shear deflection; shear = 0.422 mm

Total deflection; = bending + shear = 8.500 mm

PASS - Actual deflection within permissible limits

Loft Floor Joists

Loft Floor- Span 2.20m






mm 22001A B



175

47

50






Modification factorsService class for bending parallel to grain; K2m = 1.00

Loft Floor Joists


Service class for compression; K2c = 1.00Service class for shear parallel to grain; K2s = 1.00Service class for modulus of elasticity; K2e = 1.00Section depth factor; K7 = 1.06























Loft Floor Joists







mm 40001A B



200

47

50






Loft Floor Joists


Modification factorsService class for bending parallel to grain; K2m = 1.00Service class for compression; K2c = 1.00Service class for shear parallel to grain; K2s = 1.00Service class for modulus of elasticity; K2e = 1.00Section depth factor; K7 = 1.05























Foundation Design

Strip 1 - Central Wall

STRIP FOOTING ANALYSIS AND DESIGN (BS8110-1:1997)Tedds calculation version 2.0.07

89.4 kN/m 89.4 kN/m2 2

400

200

500

125 250 125

Strip footing detailsWidth of strip footing; B = 500 mm

Depth of strip footing; h = 400 mm

Depth of soil over strip footing; hsoil = 200 mm

Density of concrete; conc = 23.6 kN/m3

Load detailsLoad width; b = 250 mm

Load eccentricity; eP = 0 mm

Soil detailsDense, moderately graded, rounded to sub-angular, course to medium sand

Mobilisation factor; m= ;1.5;

Density of soil; soil = 20.0 kN/m3

Design shear strength; ’ = 24.2 deg

Design base friction; = 18.6 deg

Allowable bearing pressure; Pbearing = 105 kN/m2

Axial loading on strip footingDead axial load; PG = 27.0 kN/m

Imposed axial load; PQ = 11.0 kN/m

Wind axial load; PW = 0.0 kN/m

Total axial load; P = 38.0 kN/m

Foundation Design

Strip 1 - Central Wall

Foundation loadsDead surcharge load; FGsur = 0.000 kN/m2

Imposed surcharge load; FQsur = 0.000 kN/m2

Strip footing self weight; Fswt = h conc = 9.440 kN/m2

Soil self weight; Fsoil = hsoil soil = 4.000 kN/m2

Total foundation load; F = B (FGsur + FQsur + Fswt + Fsoil) = 6.7 kN/m

Calculate base reactionTotal base reaction; T = F + P = 44.7 kN/m

Eccentricity of base reaction in x; eT = (P eP + M + H h) / T = 0 mm

Base reaction acts within middle third of base

Calculate base pressuresq1 = (T / B) (1 - 6 eT / B) = 89.440 kN/m2

q2 = (T / B) (1 + 6 eT / B) = 89.440 kN/m2

Minimum base pressure; qmin = min(q1, q2) = 89.440 kN/m2

Maximum base pressure; qmax = max(q1, q2) = 89.440 kN/m2

PASS - Maximum base pressure is less than allowable bearing pressure

Material detailsCharacteristic strength of concrete; fcu = 30 N/mm2

Calculate base lengthsLeft hand length; BL = B / 2 + eP = 250 mm

Right hand length; BR = B / 2 - eP = 250 mm

Calculate rate of change of base pressureLength of base reaction; Bx = B = 500 mm

Rate of change of base pressure; Cx = (q1 - q2) / Bx = 0.000 kN/m2/m

Calculate minimum depth of unreinforced strip footingAverage pressure to left of strip footing; qL = q1 - Cx (BL - b / 2) / 2 = 89.440 kN/m2

Minimum depth to left of strip footing; hLmin = (BL-b/2)max(0.15[(qL/1 kN/m2)2/(fcu/1 N/mm2)]1/4,1) =

125 mm

Average pressure to right of strip footing; qR = q2 + Cx (BR - b / 2) / 2 = 89.440 kN/m2

Minimum depth to right of strip footing; hRmin = (BR-b/2)max(0.15[(qR/1kN/m2)2/(fcu/1N/mm2)]1/4,1) =

125 mm

Minimum depth of unreinforced strip footing; hmin = max(hLmin, hRmin, 300 mm) = 300 mm

PASS - Unreinforced strip footing depth is greater than minimum

1. This structural design is based upon information provided by the architect, should any

variation between site conditions and the information provided by the architect be

identified, this design will be void.

2. No details in this pack should be scaled.

3. All construction work should be carried out by a competent contractor.

4. The contractor is responsible for all temporary supports and is to ensure that the structure

is adequately supported during the works.

5. Steel beams are heavy components and may require mechanical lifting aids.

6. All weak or damaged masonry is to be re-built.

7. Existing foundations are assumed to be adequate, however, this is subject to exposing

the existing foundations and an inspection for the satisfaction of the Building Control

Officer.

8. Steel beam end bearing not to be inserted into a chimney or chimney breast.

9. Steel beam end bearing not to be located within 50mm of a flue.

10. .All steel is to be Grade S275 to BS EN 10025 and shall be primed with zinc rich primer

11. Steel beam end bearings to be located on mass concrete padstones.

12. Padstones to be minimum grade C30 concrete.

13. The minimum end bearing length at supports to be 100mm.

14. Supporting masonry to comply with Eurocode 6 or BS 5628.

15. New steel beams to be encased in 12.5mm Gyproc fireline board with staggered joints

nailed to timber cradles or painted in Nullifire S or similar intumescent paint to provide 1/2

hour fire resistance accordance with manufacturer's recommendations.

16. Timber to be Grade C24

17. These calculations / designs should be read in conjunction with Architects drawings.

STRUCTURAL CALCULATIONS FOR REAR EXTENSION AND LOFT … … · New Lintel L2 is to be 1No. 1950mm...

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Transcript of STRUCTURAL CALCULATIONS FOR REAR EXTENSION AND LOFT … … · New Lintel L2 is to be 1No. 1950mm...