11.03.14 final issb wall calculations
TRANSCRIPT
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Grain for Gain - Grain Storage Facility By: JDS Dat
ISSB Wall Calculations - Long Elevation
Member/Location EFOD NW Chkd: D
Drawing Ref. Sheet No. 2 of 13 Revision Appd: Dat
B
Shape Factor = 0.915
(Normalised strength of aggregate concrete blocks, Concrete Block Association, 2011)
ISSB Normalised Mean Compressive Strength (f b) = 2.313 x 0.915 = 2.115 N/mm2
Characteristic compressive strength of masonry,f k = Kf bf m
(Equation 3.1 of Eurocode 6, Part 11)
Where:
K = 0.55 (for general purpose or lightweight mortar and Group 1 Aggregate Concrete units)
(Table 3.3 of Eurocode 6, Part 11)
= 0.7 (for general purpose or lightweight mortar) = 0.3 (for general purpose or lightweight mortar)(Equation 3.2 of Eurocode 6, Part 11)
Assumed Mortar Grade: Grade iii (m4)
f m = 2.5 N/mm2
(David Almond)
f k = 0.55 x 2.115^0.7 x 2.5^0.3 = 1.223 N/mm2
Flexural strength parallel to bed joints, f kx1 0.217 N/mm2
(Interpolating From Table 1)
Flexural strength perpendicular to bed joints, f kx2 0.357 N/mm2
(Interpolating From Table 1)
M4 M4Unit
Width(mm)
Unit Height(mm)
100 0.250 100 0.400
140 0.217 140 0.357
250 0.150 250 0.250
(Assuming ISSBs approximated by aggregate concrete blocks of declared compressive strength 2.9N/mm 2)
(How to design masonry structures using Eurocode 6_Lateral Resistance, The Concrete Centre, 2007)
= f xk1 /f xk2 = 0.217/0.357 = 0.607
(How to design masonry structures using Eurocode 6_Lateral Resistance, The Concrete Centre, 2007)
m comp. = 3 (From Table 1 For unreinforced units of Class 2 and Category II)m flex. = 2.7 (From Table 1 For unreinforced units of Class 2 and Category II) shear = 2 5 (From Table 1 For unreinforced units of Class 2 and Category II)
Mortar Mortar
Calculation
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Grain for Gain - Grain Storage Facility By: JDS Dat
ISSB Wall Calculations - Long Elevation
Member/Location EFOD NW Chkd: D
Drawing Ref. Sheet No. 3 of 13 Revision Appd: Dat
B
ISSB Self Weight 18.5 kN/m 3 Ring Beam Self Weight 24 kN/m 3
(http://www.earth-auroville.com/compressed_stabilised_earth_block_en.php)
(ISSB self weight taken as the mid range for a Calss B 5% cement Compressed Stabilised Earth Block)
LOAD CASES
Vertical Load
Permanent Roof Load (G kR) = 2.2042 kN/m
Ring Beam Load (G kRB) = 0.672 kN/m ( 24 x 0.2 x 0.14 )
ISSB Wall Load at Base (G kWB) = 6.216 kN/m ( 18.5 x 2.4 x 0.14 )
ISSB Wall Load at Mid Height (G kWM) = 3.108 kN/m ( 18.5 x 1.2 x 0.14 )
Imposed Roof Load (Q k) = 1.8917 kN/m
Max Vertical Wind Load (W kv,max ) = 1.9096 kN/m (load case 2)
Min Vertical Wind Load (W kv,min ) = -1.5822 kN/m (load case 1)
Horizontal Load
Horizontal Wind Load on Wall (W kh,w ) = 0.82 kN/m2
Max Horizontal Wind Load from Roof (F h,max ) = 1.1025 kN/m (load case 2)
Min Horizontal Wind Load from Roof (F h,min ) = -0.9135 kN/m (load case 1)
(Roof and Wind Loads - EFOD Grain Store Roof Loads, James Edwards)
RESISTANCE TO FLEXURAL MOMENT
(Assumed to be most critical)
Slenderness Check
(How to design masonry structures using Eurocode 6_Lateral Resistance, The Concrete Centre, 2007)
(Figure 1)
h/t = 2.4 / 0.14 = 17.143 < 30
h/l ratio = 2.4 / 8 = 0.300 > 0.3 Two way spanning wall
(How to design masonry structures using Eurocode 6_Lateral Resistance, The Concrete Centre, 2007)
(Table 2)
Slenderness Serviceability Check
h/t = 17.143 and l/t = 8 / 0.14 = 57.143
(How to design masonry structures using Eurocode 6_Lateral Resistance, The Concrete Centre, 2007)(Figure 2)
Calculation
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Grain for Gain - Grain Storage Facility By: JDS Date:
ISSB Wall Calculations - Long Elevation
Member/Location EFOD NW Chkd: Dat
Drawing Ref. Sheet No. 4 of 13 Revision Appd: Date
B
Plane of failure parallel to bed joints
(How to design masonry structures using Eurocode 6_Lateral Resistance, The Concrete Centre, 2007)
Design Flexural Moment: M Ed1 = 1WEd l2 Where:
1: Bending moment coefficient parallel to the bed jointsWEd : Factored Horizontal Wind Load 1.5 x 0.82 = 1.23 kN/m
2
l: Height of ISSB wall = 2.400 m
1 = 2
To determine 2, Wall condition G assumed (Table 2)
Sides assumed fully restrained
Top and bottom assumed simply supported
Interpolating values of 2: (Table 2)Calculated:
h/l 0.3 0.300 0.5
0.7 0.0090 0.0090 0.0170
Calculated: 0.607 0.0099
0.6 0.0100 0.0100 0.0190
2 = 0.00991 = 2 = 0.6075 x 0.0099 = 0.006
MEd1 = 1WEd l2 = 0.006 x 1.23 x 2.4^2 = 0.042717 kNm/m
Design Flexural Resistance
(How to design masonry structures using Eurocode 6_Lateral Resistance, The Concrete Centre, 2007)
MRd1 = (f xk1/M + d )Z (d
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Grain for Gain - Grain Storage Facility By: JDS Date:
ISSB Wall Calculations - Long Elevation
Member/Location EFOD NW Chkd: Dat
Drawing Ref. Sheet No. 5 of 13 Revision Appd: Date
B
Z = section modulus of the plan shape of the wall
f k = characteristic compressive strength (see Vertical resistance3).
f xk1 = 0.217
M = 2.7d = design vertical load per unit area at mid height:d = F/AF = 1.0G k + 1.5W k (W k = minimum vertical wind load)
Gk = G kR + G kRB + G kWM = 2.204 + 0.672 + 3.108 = 5.9842 kN/m
F = 5.984 + (1.5 x -1.582) = 3.611 kN/m
d = 3.611 / 0.14 = 25.79 kN/m2 = 0.0258 N/mm 2
0.2f k/M = 0.2 x 1.223 / 2.7 = 0.0906 N/mm2 > d
Z = bh 2/6 = 1 x t ef12/6
f k = 1.223
For wall to pass in flexure t ef needs to be sufficient that M Rd > MEd
(f xk1/M + d )Z > M Ed(0.217 / 2.7 + 0.026) x (tef1^2)/6 > 0.043
tef1 = {(1000 x 6 x 0.043) / (0.217 / 2.7 + 0.026)}
tef1 = 49.163 mm
Plane of failure perpendicular to bed joints
(How to design masonry structures using Eurocode 6_Lateral Resistance, The Concrete Centre, 2007)
Design Flexural Moment: M Ed2 = 2WEd l2 = 0.0099 x 1.23 x 8^2 = 0.7813 kNm/m
Design Flexural Resistance
MRd2 = (f xk2/M)Z > M Ed(0.357 / 2.7) x (tef2^2)/6 > 0.781
tef2 = {(1000 x 6 x 0.781) / (0.357 / 2.7)}
tef2 = 188.38 mm
max t ef = tef2 = 188.4 mm
tef
S
Calculation
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Grain for Gain - Grain Storage Facility By: JDS Date
ISSB Wall Calculations - Long Elevation
Member/Location EFOD NW Chkd: Da
Drawing Ref. Sheet No. 7 of 13 Revision Appd: Date
B
RESISTANCE TO VERTICAL LOAD
Minimum Area Check
(How to design masonry structures using Eurocode 6_Vertical Resistance, The Concrete Centre, 2007)
(Figure 1)
Area per metre length = 0.14 x 1 = 0.14 m 2 0.04 m 2
Slenderness Check
(How to design masonry structures using Eurocode 6_Vertical Resistance, The Concrete Centre, 2007)
(Figure 1)
= h ef /tef = 2.6 / 0.177 = 14.698 27
Load Cases
Load Case = 1.35G k + 1.05Q k + 1.5W k
NEd = 1.35(2.204 + 0.672 + 6.216) + 1.05(1.892) + 1.5(1.91) = 16.067 kN/m
Capacity Reduction Factor (Check to see if Simplified Version can be used)
Simplified version can only be used if: t (c1qEwdbh2)/N Ed +c2h where:
(Equation 4.2, BS EN 1996-3:2006)
h: clear storey height
qEwd : design wind load on the wall per unit area of wall
NEd : design value of vertical load giving the least severe effect on wall at top of the storey considered
b: width over which the vertical load is effective
t: actual thickness of the wall
: Ned/tbf df d: design compressive strength of the masonry
c1 ,c 2: constants dervied from Table 4.1
h = 2.4 + 0.2 = 2.600 m b = 0.14 m
Calculation
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Grain for Gain - Grain Storage Facility By: JDS Date
ISSB Wall Calculations - Long Elevation
Member/Location EFOD NW Chkd: Da
Drawing Ref. Sheet No. 8 of 13 Revision Appd: Date
B
To calculate N Ed : Load Case: 1.0G k + 1.5W k (W k = minimum wind load)
G k = Gk R + Gk RB = 2.204 + 0.672 = 2.8762 kN/m
Wk = -1.582 kN/m
Ned = 1 x 2.876 + 1.5 x -1.582 = 0.5028 kN/m
= 0.503 / (0.14 x 0.14 x 407.722) = 0.0629
Interpolating from Table 4.1
c1 c20.05 0.12 0.017
0.063 0.120 0.018
0.1 0.12 0.019
c1: 0.120
c2: 0.0175
Therefore: (c1qEwdbh2)/N Ed +c2h = (0.12 x 1.23 x 0.14 x 2.6^2) / 0.503 + 0.018 x 2.6
= 0.3234 >t
Capacity Reduction Factor (Top and Bottom of Wall)
i = 1 - 2(e i/t)(Equation 6.4, BS EN 1996-1-1:2005+A1:2012)
e i = M id/N id + e he + e init 0.05t
(Equation 6.5, BS EN 1996-1-1:2005+A1:2012)
(6.1.2.2, BS EN 1996-1-1:2005+A1:2012)
Mid: Design bending moment at the top or bottom of wall resulting from the eccentricity of roof load at support.
Nid: Design value of the vertical load at the top or bottom of the wall
e he : is the eccentricity at the to or bottom of the wall, if any, resulting from horizontal loads
e init: is the initial eccentricity
t: Thickness of the wall
Mid = 0 kNm/ (Assumed : No eccentricity of loading from roof truss, no loading at bottom of wall )
Nidbottom = 16.067 kN/m (Taken as N Ed for vertical resistance)
Nidtop = N idbottom - 1.35 x G kWB 16.067 - 1.35 x 6.216 = 7.676 kN/m
e he = (w kh2/12)/N id (assuming encastre ends which give worst case moment at top and bottom of wall)
Calculation
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Grain for Gain - Grain Storage Facility By: JDS Dat
ISSB Wall Calculations - Long Elevation
Member/Location EFOD NW Chkd: D
Drawing Ref. Sheet No. 9 of 13 Revision Appd: Dat
B
(DOES MOMENT FROM HORIZONTAL ROOF WIND NEED TO BE CONSIDERED?)
e hebottom = 1000 x (1.5 x 0.82 x 2.4^2 / 12) / 16.067 = 36.745 mm
e hetop = 1000 x (1.5 x 0.82 x 2.4^2 / 12) / 7.676 = 76.918 mm
e init = h ef /450 = 1000 x 2.6 / 450 = 5.778 mm
(How to design masonry structures using Eurocode 6_Vertical Resistance, The Concrete Centre, 2007)
e ibottom = M id/N idbottom + e hebotto 0 + 36.745 + 5.778 = 42.523 mm > 0.05t = 7 mm
e itop = M id/N idtop + e hetop + e init 0 + 76.918 + 5.778 = 82.695 mm > 0.05t = 7 mm
(6.1.2.2, BS EN 1996-1-1:2005+A1:2012)
ibottom = 1-2 x (42.523 / 140) = 0.39253
itop = 1-2 x (82.695 / 140) = -0.18136
THIS SEEMS INFEASIBLE?
Capacity Reduction Factor (Middle of Wall)
e mk = e m + e k 0.05t where:
(Equation 6.6, BS EN 1996-1-1:2005+A1:2012)
e mk = is the eccentricity at the middle height of the wall
e m = is the eccentricity due to loads
e k = is the eccentricity due to creep,
e k can be ignored as slenderness ration ( ) < 27 (i.e can ignore creep)
(How to design masonry structures using Eurocode 6_Vertical Resistance, The Concrete Centre, 2007)
e m = M md /Nmd + e hm + e init Where:
(Equation 6.7, BS EN 1996-1-1:2005+A1:2012)
Nmd = The design value of the vertical load at the middle height of the wall, including any load applied
eccentrically to the face of the wall.
Mmd = The design value of the greatest moment at the middle of the height of the wall resulting from the
moments at the top and bottom of the wall including any load applied eccentrically to the face of the wall.
e hm = The eccentricity at mid-height resulting from horizontal loads (for example, wind);
e m = The eccentricity due to loads;
Calculation
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Grain for Gain - Grain Storage Facility By: JDS Date:
ISSB Wall Calculations - Long Elevation
Member/Location EFOD NW Chkd: Dat
Drawing Ref. Sheet No. 10 of 13 Revision Appd: Date
B
Nmd = 1 x (2.204 + 0.672 + 3.108) + 1.5 x -1.582 = 3.611 kN/m
Mmd = 0 kNm/m
(ASSUMED NO MID HEIGHT MOMENT FROM TOP AND BOTTOM MOMENTS - IS THIS CORRECT?)
e hm = 1.5w kh2/8 = ((1.5 x 0.82 x 2.4^2) / 8) / 3.611 = 0.245 m
= 245.263 mm
(worst case - wall assumed simply supported)
(Example 6, www.eurocode6.org/Design%20Examples.htm)
e m = 0 / 3.611 + 245.263 +5.778 = 251.0404 mm = 1.793 t
THIS IS OFF THE SCALE OF FIGURE 8.
WOULD BE OFF THE SCALE EVEN IF wh 2 /24 USED AS MID HEIGHT MOMENT FORMULA.
(How to design masonry structures using Eurocode 6_Vertical Resistance, The Concrete Centre, 2007)
m = ???
NRd = ??? kN/m
Calculation
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Grain for Gain - Grain Storage Facility By: JDS Date:
ISSB Wall Calculations - Long Elevation
Member/Location EFOD NW Chkd: Dat
Drawing Ref. Sheet No. 11 of 13 Revision Appd: Date
B
Capacity Reduction Factor (Simplified Version)
(CALCULATED ANYWAY DESPITE NOT PASSING THE REQUIRED CHECK)
s = capacity reduction factor allowing for the effects of slenderness and eccentricity in loading.s = lesser of sa , sb , sc for walls at the highest level acting as end supports to roof.(Clause 4.2.2.3, BS EN 1996-3:2006)
sa = 0.85 - 0.0011(h ef /tef )2 = 0.85 - 0.0011 x (2.6 / 0)^2 = 0.612(Equation 4.5a, BS EN 1996-3:2006)
sb = 1.3 - l f,ef /8 0.85 where l f,ef is the effective span of the floor = floor span (simply supported)(Equation 4.5b, BS EN 1996-3:2006)
lf,ef = 6.300 m
sb = 1.3 - 6.3 / 8 = 0.5125 < 0.85
sc = 0.4(Equation 4.5c, BS EN 1996-3:2006)
s = 0.400
0.4 SEEMS A CONSERVATIVE CAPACITY REDUCTION FACTOR
0.4 IS LESS THAN THE VALUE CALCULATED FOR I
0.4 USED EVEN THOUGH REQUIRED CHECK NOT PASSED
Design Vertical Resistance
NRd = sfdA(Equation 4.4, BS EN 1996-3:2006)
NRd = s(f k/m)t = 0.4 x (1000 x 1.223 / 3) x 0.14 = 22.832 kN/mNEd = 16.067 kN/m
Safety Margin = 1.421
NRd > NEd Wall Passes in Compression OK
Calculation
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Grain for Gain - Grain Storage Facility By: JDS Date:
ISSB Wall Calculations - Long Elevation
Member/Location EFOD NW Chkd: Date
Drawing Ref. Sheet No. 12 of 13 Revision Appd: Date
B
RESISTANCE TO SHEAR
Assuming wall acts as cantilever with uniformly distributed wind load and point load at top applied by roof.
Fv
Fh
GkWB Wkh
Applied Shear Force
Shear Load Case: 1.0G k + 1.5W k (Load Case1)
Wkh = 0.820 kN/m2
GkWB = 6.216 kN/m
Fh = F h,min 0.914 kN/m
Fv = G kR + G kRB + W kv,min
VEd = 1.5 x (h x W k + F h) = 1.5 x (2.6 x 0.82 + 0.914) = 4.568 kN/m
Characteristic Shear Strength of Masonry
Perpend Joint Type: Unfilled (Worst Case)
Pier Stiffening Included: No (Worst Case)
fvk = 0.5fvk0 + 0.4d 0.045fb
(How to design masonry structures using Eurocode 6_Lateral Resistance, The Concrete Centre, 2007)
Where: f vk = characteristic shear strength of masonry
f vk0 = characteristic initial shear strength of masonry under zero compressive stress
f b = normalised compressive strength of the masonry unitsd = design compressive stress perpendicular to the shear d = F/AF= 1.0 x (G kR+G kRB +G kWB) + 1.5 x W k,min
( )
Calculation
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Grain for Gain - Grain Storage Facility By: JDS Date: 1
ISSB Wall Calculations - Long Elevation
Member/Location EFOD NW Chkd: Date
Drawing Ref. Sheet No. 13 of 13 Revision Appd: Date
B
d = 6.719 / (1 x 0.14) = 47.992 kN/m2 = 0.048 N/mm 2
f vk0 = 0.15 N/mm2 (Table 3)
(How to design masonry structures using Eurocode 6_Lateral Resistance, The Concrete Centre, 2007)
(Worst case for aggregate concrete masonry unit, general purpose m4 mortar)
fvk = 0.5 x 0.15 + 0.4 x 0.048 = 0.094 N/mm 2 < 0.045 x 2.115 = 0.095 N/mm 2 O
Design Shear Resistance
VRd = fvk/M x t = 0.095 / 2.5 x 140 = 5.330 kN/m
VEd = 4.56825 kN/m
Safety Margin = 1.166797
VRd > VEd Wall Passes in Shear OK
DOES WHOLE STRUCTURE STABILITY NEED TO BE CONSIDERED?
Calculation
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Grain for Gain - Grain Storage Facility By: JDS Date: 16/03/14
ISSB Wall Calculations - Gable End
Member/Location EFOD NW Chkd: Date:
Drawing Ref. Sheet No. 1 of 13 Revision Appd: Date
B
Long Elevation
6.300 m
2.400 m
MASONRY CHARACTERISTICS
Category: II (lower level of confidence in compressive st rength)
(http://www.eurocode6.org/FAQ%203.htm)
Group: 1 (< 25% formed vertical voids by volume)
(Understanding BS EN 771-3: Aggregate Concrete Blocks, Concrete Block Association, 2006)
Class: 2 (Lower standards of execution)
(NA.2.1, NA to BS EN 1996-1-1:2005+A1:2012)
Dimensions
Height = 0.1 m Ring Beam Height = 0.2 m
Length = 0.29 m (maximum extent)
Width = 0.14 m
(ISSB Construction Handbook, Good Earth Trust, 2010)
Strength
ISSB Mean Compressive Strength = 2.313 N/mm 2
(ISSB Compression Test Makerere University)
ISSB Normalised Mean Compressive Strength = Mean Compressive Strength x Shape Factor
(Interpolating From Table 1)
Unit Width (mm) 140UnitHeight
(mm)
Calculation Output
(Reinforced Concrete Ring Beam)
ISSB Wall
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Grain for Gain - Grain Storage Facility By: JDS Date: 16/03/14
ISSB Wall Calculations - Gable End
Member/Location EFOD NW Chkd: Date:
Drawing Ref. Sheet No. 2 of 13 Revision Appd: Date
B
Shape Factor = 0.915
(Normalised strength of aggregate concrete blocks, Concrete Block Association, 2011)
ISSB Normalised Mean Compressive Strength (f b) = 2.313 x 0.915 = 2.115 N/mm2
Characteristic compressive strength of masonry,f k = Kf bf m
(Equation 3.1 of Eurocode 6, Part 11)
Where:
K = 0.55 (for general purpose or lightweight mortar and Group 1 Aggregate Concrete units)
(Table 3.3 of Eurocode 6, Part 11)
= 0.7 (for general purpose or lightweight mortar) = 0.3 (for general purpose or lightweight mortar)(Equation 3.2 of Eurocode 6, Part 11)
Assumed Mortar Grade: Grade iii (m4)
f m = 2.5 N/mm2
(David Almond)
f k = 0.55 x 2.115^0.7 x 2.5^0.3 = 1.223 N/mm2
Flexural strength parallel to bed joints, f kx1 0.217 N/mm2
(Interpolating From Table 1)
Flexural strength perpendicular to bed joints, f kx2 0.357 N/mm2
(Interpolating From Table 1)
M4 M4UnitWidth(mm)
Unit Height(mm)
100 0.250 100 0.400140 0.217 140 0.357
250 0.150 250 0.250
(Assuming ISSBs approximated by aggregate concrete blocks of declared compressive strength 2.9N/mm 2)
(How to design masonry structures using Eurocode 6_Lateral Resistance, The Concrete Centre, 2007)
= f xk1/f xk2 = 0.217/0.357 = 0.607(How to design masonry structures using Eurocode 6_Lateral Resistance, The Concrete Centre, 2007)
m comp. = 3 (From Table 1 For unreinforced units of Class 2 and Category II)
Calculation Output
Mortar Mortar
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m flex. = 2.7 (From Table 1 For unreinforced units of Class 2 and Category II)m shear. = 2.5 (From Table 1 For unreinforced units of Class 2 and Category II)(How to design masonry structures using Eurocode 6_Introduction, The Concrete Centre, 2007)
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Grain for Gain - Grain Storage Facility By: JDS Date: 16/03/14
ISSB Wall Calculations - Gable End
Member/Location EFOD NW Chkd: Date:
Drawing Ref. Sheet No. 3 of 13 Revision Appd: Date
B
ISSB Self Weight 18.5 kN/m 3 Ring Beam Self Weight 24 kN/m 3
(http://www.earth-auroville.com/compressed_stabilised_earth_block_en.php)
(ISSB self weight taken as the mid range for a Calss B 5% cement Compressed Stabilised Earth Block)
LOAD CASES
Vertical Load
Permanent Roof Load (G kR) = 0 kN/m
Ring Beam Load (G kRB) = 0.672 kN/m ( 24 x 0.2 x 0.14 )
ISSB Wall Load at Base (G kWB) = 6.216 kN/m ( 18.5 x 2.4 x 0.14 )
ISSB Wall Load at Mid Height (G kWM) = 3.108 kN/m ( 18.5 x 1.2 x 0.14 )
Imposed Roof Load (Q k) = 0 kN/m
Max Vertical Wind Load (W kv,max ) = 0 kN/m (load case 2)
Min Vertical Wind Load (W kv,min ) = 0 kN/m (load case 1)
Horizontal Load
Horizontal Wind Load on Wall (W kh,w ) = 0.82 kN/m2
Max Horizontal Wind Load from Roof (Fh,max
) = 0 kN/m (load case 2)
Min Horizontal Wind Load from Roof (F h,min ) = 0 kN/m (load case 1)
(Roof and Wind Loads - EFOD Grain Store Roof Loads, James Edwards)
RESISTANCE TO FLEXURAL MOMENT
(Assumed to be most critical)
Slenderness Check
(How to design masonry structures using Eurocode 6_Lateral Resistance, The Concrete Centre, 2007)
(Figure 1)
h/t = 2.4 / 0.14 = 17.143 < 30 OK
h/l ratio = 2.4 / 6.3 = 0.381 > 0.3 Two way spanning wall
(How to design masonry structures using Eurocode 6_Lateral Resistance, The Concrete Centre, 2007)
(Table 2)
Slenderness Serviceability Check
h/t = 17.143 and l/t = 6.3 / 0.14 = 45 OK
(How to design masonry structures using Eurocode 6_Lateral Resistance, The Concrete Centre, 2007)
(Figure 2)
Calculation Output
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Grain for Gain - Grain Storage Facility By: JDS Date: 16/03/14
ISSB Wall Calculations - Gable End
Member/Location EFOD NW Chkd: Date:
Drawing Ref. Sheet No. 4 of 13 Revision Appd: Date
B
Plane of failure parallel to bed joints
(How to design masonry structures using Eurocode 6_Lateral Resistance, The Concrete Centre, 2007)
Design Flexural Moment: M Ed1 = 1WEd l2 Where:
1: Bending moment coeffic ient parallel to the bed jointsWEd : Factored Horizontal Wind Load 1.5 x 0.82 = 1.23 kN/m
2
l: Height of ISSB wall = 2.400 m
1 = 2
To determine 2, Wall condition G assumed (Table 2)
Sides assumed fully restrained
Top and bottom assumed simply supported
Interpolating values of 2: (Table 2)Calculated:
h/l 0.3 0.381 0.5
0.7 0.0090 0.0122 0.0170
Calculated: 0.607 0.0132
0.6 0.0100 0.0136 0.0190
2 = 0.01321 = 2 = 0.6075 x 0.0132 = 0.008
MEd1 = 1WEd l2 = 0.008 x 1.23 x 2.4^2 = 0.056653 kNm/m
Design Flexural Resistance
(How to design masonry structures using Eurocode 6_Lateral Resistance, The Concrete Centre, 2007)
MRd1 = (f xk1/M + d )Z (d
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f xk1 = characteristic flexural strength of masonry bending axis parallel to bed jointsabout an axis parallel to bed joints
M = appropriate partial factor for materialsd = design vertical load per unit area
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Grain for Gain - Grain Storage Facility By: JDS Date: 16/03/14
ISSB Wall Calculations - Gable End
Member/Location EFOD NW Chkd: Date:
Drawing Ref. Sheet No. 5 of 13 Revision Appd: Date
B
Z = section modulus of the plan shape of the wall
f k = characteristic compressive strength (see Vertical resistance3).
f xk1 = 0.217
M = 2.7d = design vertical load per unit area at mid height:d = F/AF = 1.0G k + 1.5W k (Wk = minimum vertical wind load)
G k = G kRB + G kWM = 0.672 + 3.108 = 3.78 kN/m
F = 3.78 + (1.5 x 0) = 3.780 kN/m
d = 3.78 / 0.14 = 27 kN/m 2 = 0.027 N/mm 2
0.2f k/M = 0.2 x 1.223 / 2.7 = 0.0906 N/mm2 > d OK
Z = bh 2/6 = 1 x t ef12/6
f k = 1.223
For wall to pass in flexure t ef needs to be sufficient that M Rd > M Ed
(f xk1/M + d )Z > M Ed(0.217 / 2.7 + 0.027) x (tef1^2)/6 > 0.057
tef1 = {(1000 x 6 x 0.057) / (0.217 / 2.7 + 0.027)}tef1 = 56.298 mm
Plane of failure perpendicular to bed joints
(How to design masonry structures using Eurocode 6_Lateral Resistance, The Concrete Centre, 2007)
Design Flexural Moment: M Ed2 = 2W Ed l2 = 0.0132 x 1.23 x 6.3^2 = 0.6426 kNm/m
Design Flexural Resistance
MRd2 = (f xk2/M)Z > M Ed(0.357 / 2.7) x (tef2^2)/6 > 0.643
tef2 = {(1000 x 6 x 0.643) / (0.357 / 2.7)}
tef2 = 170.84 mm
max t ef = tef2 = 170.8 mm
tef
S
Calculation Output
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Thus, required effective thickness of wall = 170.8 mm
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Grain for Gain - Grain Storage Facility By: JDS Date: 16/03/14
ISSB Wall Calculations - Gable End
Member/Location EFOD NW Chkd: Date:
Drawing Ref. Sheet No. 6 of 13 Revision Appd: Date
B
The effective thickness of a wall stiffensed by piers is given by: p t x t , where:
t = thickness of wall = 0.14 m
pt = ratio determines from table 5.1 of EC5-1-1 below;
Try pier spacing = 3.15 m
Pier width = 0.29 m Spacing / Width = 10.862 (A in table below)
Pier depth = 0.29 m Pier / wall thickness = 2.0714 (B in table below)
Interpolating values of p t: (Table 5.1, EC5-1-1)
Calculated:B 2 2.071 3
A
6 1.4000 1.4429 2.0000
Calculated: 10.862 1.1650
10 1.2000 1.2143 1.4000 0.163
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Grain for Gain - Grain Storage Facility By: JDS Date: 16/03/14
ISSB Wall Calculations - Gable End
Member/Location EFOD NW Chkd: Date:
Drawing Ref. Sheet No. 7 of 13 Revision Appd: Date
B
RESISTANCE TO VERTICAL LOAD
Minimum Area Check
(How to design masonry structures using Eurocode 6_Vertical Resistance, The Concrete Centre, 2007)
(Figure 1)
Area per metre length = 0.14 x 1 = 0.14 m 2 0.04 m 2 OK
Slenderness Check
(How to design masonry structures using Eurocode 6_Vertical Resistance, The Concrete Centre, 2007)
(Figure 1)
= h ef /tef = 2.6 / 0.163 = 15.9408 27 OK
Load Cases
Load Case = 1.35G k
NEd = 1.35(0.672 + 6.216) = 9.2988 kN/m
Capacity Reduction Factor (Check to see if Simplified Version can be used)
Simplified version can only be used if: t (c1qEwdbh 2)/N Ed +c2h where:
(Equation 4.2, BS EN 1996-3:2006)
h: clear storey height
qEwd : design wind load on the wall per unit area of wall
NEd : design value of vertical load giving the least severe effect on wall at top of the storey considered
b: width over which the vertical load is effective
t: actual thickness of the wall
: Ned/tbf df d: design compressive strength of the masonry
c1,c 2: constants dervied from Table 4.1
Calculation Output
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h = 2.4 + 0.2 = 2.600 m b = 0.14 m
qEwd = 1.5 x 0.82 = 1.23 kN/m2/m 2 t = 0.14 m
f d = 1223 / 3 = 407.722 kN/m2
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Grain for Gain - Grain Storage Facility By: JDS Date: 16/03/14
ISSB Wall Calculations - Gable End
Member/Location EFOD NW Chkd: Date:
Drawing Ref. Sheet No. 8 of 13 Revision Appd: Date
B
To calculate N Ed : Load Case: 1.0G k + 1.5W k (Wk = minimum wind load)
Gk = Gk RB = 0.672 kN/m
Wk = 0 kN/m
Ned = 1 x 0.672 = 0.672 kN/m
= 0.672 / (0.14 x 0.14 x 407.722) = 0.0841
Interpolating from Table 4.1
c1 c20.05 0.12 0.017
0.084 0.120 0.018
0.1 0.12 0.019
c1: 0.120
c2: 0.0184
Therefore: (c1qEwdbh 2)/N Ed +c2h = (0.12 x 1.23 x 0.14 x 2.6^2) / 0.672 + 0.018 x 2.6 Cannot Use
= 0.25562 >t Simplified
Version
Capacity Reduction Factor (Top and Bottom of Wall)
i = 1 - 2(e i/t)(Equation 6.4, BS EN 1996-1-1:2005+A1:2012)
e i = M id/Nid + e he + e init 0.05t
(Equation 6.5, BS EN 1996-1-1:2005+A1:2012)
(6.1.2.2, BS EN 1996-1-1:2005+A1:2012)
Mid: Design bending moment at the top or bottom of wall resulting from the eccentricity of roof load at support.
Nid: Design value of the vertical load at the top or bottom of the wall
e he : is the eccentricity at the to or bottom of the wall, if any, resulting from horizontal loads
e init: is the initial eccentricity
t: Thickness of the wall
Mid = 0 kNm/m (Assumed : No eccentricity of loading from roof truss, no loading at bottom of wall )
Nidbottom = 9.2988 kN/m (Taken as N Ed for vertical resistance)
Nidtop = N idbottom - 1.35 x G kWB 9.299 - 1.35 x 6.216 = 0.907 kN/m
Calculation Output
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e he = (w kh2/12)/N id (assuming encastre ends which give worst case moment at top and bottom of wall)
(Example 6, www.eurocode6.org/Design%20Examples.htm)
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Grain for Gain - Grain Storage Facility By: JDS Date: 16/03/14
ISSB Wall Calculations - Gable End
Member/Location EFOD NW Chkd: Date:
Drawing Ref. Sheet No. 9 of 13 Revision Appd: Date
B
(DOES MOMENT FROM HORIZONTAL ROOF WIND NEED TO BE CONSIDERED?)
e hebottom = 1000 x (1.5 x 0.82 x 2.4^2 / 12) / 9.299 = 63.492 mm
e hetop = 1000 x (1.5 x 0.82 x 2.4^2 / 12) / 0.907 = 650.794 mm
e init = h ef /450 = 1000 x 2.6 / 450 = 5.778 mm
(How to design masonry structures using Eurocode 6_Vertical Resistance, The Concrete Centre, 2007)
e ibottom = M id/N idbottom + e hebotto 0 + 63.492 + 5.778 = 69.270 mm > 0.05t = 7 mm
e itop = M id/N idtop + e hetop + e init 0 + 650.794 + 5.778 = 656.571 mm > 0.05t = 7 mm
(6.1.2.2, BS EN 1996-1-1:2005+A1:2012)
ibottom = 1-2 x (69.27 / 140) = 0.01043
itop = 1-2 x (656.571 / 140) = -8.37959
THIS IS IMPOSSBLE?
Capacity Reduction Factor (Middle of Wall)
e mk = e m + e k 0.05t where:
(Equation 6.6, BS EN 1996-1-1:2005+A1:2012)
e mk = is the eccentricity at the middle height of the wall
e m = is the eccentricity due to loads
e k = is the eccentricity due to creep,
e k can be ignored as slenderness ration ( ) < 27 (i.e can ignore creep)
(How to design masonry structures using Eurocode 6_Vertical Resistance, The Concrete Centre, 2007)
em
= Mmd
/Nmd
+ ehm
+ einit
Where:
(Equation 6.7, BS EN 1996-1-1:2005+A1:2012)
Nmd = The design value of the vertical load at the middle height of the wall, including any load applied
eccentrically to the face of the wall.
Mmd = The design value of the greatest moment at the middle of the height of the wall resulting from the
moments at the top and bottom of the wall including any load applied eccentrically to the face of the wall.
e hm = The eccentricity at mid-height resulting from horizontal loads (for example, wind);
e m = The eccentricity due to loads;
Calculation Output
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Load Case: 1.0G k + 1.5W k (W k = minimum wind load)
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Grain for Gain - Grain Storage Facility By: JDS Date: 16/03/14
ISSB Wall Calculations - Gable End
Member/Location EFOD NW Chkd: Date:
Drawing Ref. Sheet No. 10 of 13 Revision Appd: Date
B
Nmd = 1 x (0 + 0.672 + 3.108) + 1.5 x 0 = 3.780 kN/m
Mmd = 0 kNm/m
(ASSUMED NO MID HEIGHT MOMENT FROM TOP AND BOTTOM MOMENTS - IS THIS CORRECT?)
e hm = 1.5w kh2/8 = ((1.5 x 0.82 x 2.4^2) / 8) / 3.78 = 0.234 m
= 234.286 mm
(worst case - wall assumed simply supported)
(Example 6, www.eurocode6.org/Design%20Examples.htm)
e m = 0 / 3.78 + 234.286 +5.778 = 240.0635 mm = 1.715 t
THIS IS OFF THE SCALE OF FIGURE 8.
WOULD BE OFF THE SCALE EVEN IF wh 2 /24 USED AS MID HEIGHT MOMENT FORMULA.
(How to design masonry structures using Eurocode 6_Vertical Resistance, The Concrete Centre, 2007)
m = ???
NRd = ??? kN/m
Calculation Output
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Grain for Gain - Grain Storage Facility By: JDS Date: 16/03/14
ISSB Wall Calculations - Gable End
Member/Location EFOD NW Chkd: Date:
Drawing Ref. Sheet No. 11 of 13 Revision Appd: Date
B
Capacity Reduction Factor (Simplified Version)
(CALCULATED ANYWAY DESPITE NOT PASSING THE REQUIRED CHECK)
s = capacity reduction factor allowing for the effects of slenderness and eccentricity in loading.s = lesser of sa , sb , sc for walls at the highest level acting as end supports to roof.(Clause 4.2.2.3, BS EN 1996-3:2006)
sa = 0.85 - 0.0011(h ef /tef )2 = 0.85 - 0.0011 x (2.6 / 0)^2 = 0.570(Equation 4.5a, BS EN 1996-3:2006)
sb = 1.3 - l f,ef /8 0.85 where l f,ef is the effective span of the floor = floor span (simply supported)(Equation 4.5b, BS EN 1996-3:2006)
lf,ef = 6.300 m
sb = 1.3 - 6.3 / 8 = 0.5125 < 0.85
sc = 0.4(Equation 4.5c, BS EN 1996-3:2006)
s = 0.400
0.4 SEEMS A CONSERVATIVE CAPACITY REDUCTION FACTOR
0.4 USED EVEN THOUGH REQUIRED CHECK NOT PASSED
Design Vertical Resistance
NRd = sfdA(Equation 4.4, BS EN 1996-3:2006)
NRd = s(f k/m)t = 0.4 x (1000 x 1.223 / 3) x 0.14 = 22.832 kN/mNEd = 9.299 kN/m
Safety Margin = 2.455
NRd > NEd Wall Passes in Compression OK
Calculation Output
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Grain for Gain - Grain Storage Facility By: JDS Date: 16/03/14
ISSB Wall Calculations - Gable End
Member/Location EFOD NW Chkd: Date:
Drawing Ref. Sheet No. 12 of 13 Revision Appd: Date
B
RESISTANCE TO SHEAR
Assuming wall acts as cantilever with uniformly distributed wind load and point load at top applied by roof.
Fv
Fh
G kWB Wkh
Applied Shear ForceShear Load Case: 1.0G k + 1.5W k (Load Case1)
Wkh = 0.820 kN/m2
G kWB = 6.216 kN/m
Fh = F h,min 0.000 kN/m
Fv = G kR + G kRB + W kv,min
VEd = 1.5 x (h x W k + F h) = 1.5 x (2.6 x 0.82 + 0) = 3.198 kN/m
Characteristic Shear Strength of MasonryPerpend Joint Type: Unfilled (Worst Case)
Pier Stiffening Included: No (Worst Case)
fvk = 0.5fvk0 + 0.4d 0.045fb
(How to design masonry structures using Eurocode 6_Lateral Resistance, The Concrete Centre, 2007)
Where: f vk = characteristic shear strength of masonry
f vk0 = characteristic initial shear strength of masonry under zero compressive stress
f b = normalised compressive strength of the masonry units
d = design compressive stress perpendicular to the shear
d = F/A
Calculation Output
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F= 1.0 x (G kR+G kRB+G kWB) + 1.5 x W k,min
F= 1.0 x (0 + 0.672 + 6.216) + 1.5 x 0
F= 6.888 kN/m
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Grain for Gain - Grain Storage Facility By: JDS Date: 16/03/14
ISSB Wall Calculations - Gable End
Member/Location EFOD NW Chkd: Date:
Drawing Ref. Sheet No. 13 of 13 Revision Appd: Date
B
d = 6.888 / (1 x 0.14) = 49.2 kN/m2 = 0.0492 N/mm 2
f vk0 = 0.15 N/mm2 (Table 3)
(How to design masonry structures using Eurocode 6_Lateral Resistance, The Concrete Centre, 2007)
(Worst case for aggregate concrete masonry unit, general purpose m4 mortar)
fvk = 0.5 x 0.15 + 0.4 x 0.049 = 0.095 N/mm 2 < 0.045 x 2.115 = 0.095 N/mm 2 OK
Design Shear Resistance
VRd = fvk/M x t = 0.095 / 2.5 x 140 = 5.330 kN/m
VEd = 3.198 kN/m
Safety Margin = 1.666735
VRd > VEd Wall Passes in Shear OK
DOES WHOLE STRUCTURE STABILITY NEED TO BE CONSIDERED?
Calculation Output