This calculation covers the design of the formwork for the construction of pile caps.
Reference
a) BS:5975:1996 Code of practice for falsework
b) Code of practice for the structural use of steel 2011
c) Steel designers manual - 5th edition
d) Formwork - a guide to good practice
Design data and assumption
a) Plywood : 18mm thk. Birch-faced
Bending stiffness, EI = 3.02 kNm^2/m
Moment of resistance, fZ = 0.655 kNm/m
Shear load, qA = 10.534 kN/m
b) Joist : 50mm x 100mm timber @300mm c/c grade SC3
Permissible bending stress, Pb = 7.1 N/mm^2
Permissible compressive stress, Pc = 2.63 N/mm^2
Permissible shear stress, Pq = 1.32 N/mm^2
Modulus of elasticity, E = 7600 N/mm^2
c) Railing : 2nos. 50mm x 26mm x 1.4mm thk. steel R.H.S grade S275
Design strength, py = 275 N/mm^2
Modulus of elasticity, E = 205000 N/mm^2
d) Anchor : Y12 steel bar Grade 460
Tensile stress, Pt = 0.87 x 460 = 400 N/mm^2
Shear stress, Pq = 0.6 x 460 = 276 N/mm^2
e) Washer : 8mm thk. steel plate grade S275
Tensile stress, py = 275 N/mm^2
Modulus of elastricity, E = 205000 N/mm^2
Concrete pressure estimation
The maximum concrete pressure on formwork is given by:
Pmax = D*[C1*R^0.5 + C2*K*(H - C1*R^0.5)^0.5]
where:
C1 = coefficient dependent on the size and shape of formwork
C2 = coefficient dependent on the constituent materials of the concrete
D = weight density of concrete
H = vertical form height
K = temperature coefficient taken as [36 / (T + 16)]^2
R = the rate at which the concrete rises vertically up the form
T = concrete temperature at placing
example case,
C1 = 1.0, C2 = 0.3, D = 24, H = 4.0, K = 0.612, R = 0.5, T = 30
C1*R^0.5 = 0.707 m (< H = 4.0m)
Pmax = 24 x [1 x 0.5^0.5 + 0.3 x 0.612 x (4 - 1 x 0.5^0.5)^0.5] = 24.97 kPa
Plywood check
Thickness of plywood, t = 18mm
Width of backing beam, B = 50mm
Maximum span, L = 300 mm
Max. pressure, Pmax = 24.97 kPa
Max. force on one span sheathing, W = Pmax*L = 7.492 kN/m
Check bending moment:
Max. bending moment, M = 0.095WL = 0.214 kNm/m < 0.655 kNm/m, OK!
Check shear:
Max. shear force, V = 0.525W(L-B-T)/L = 3.042 kN/m < 10.534 kN/m, OK!
Check deflection:
Max. deflection, d = 0.0066WL^3/EI = 0.442 mm < L/270 = 1.11 mm, OK!
Joist check
Section size of timber joist, b = 50 mm, h = 100 mm
Spacing, S = 300 mm
Elastic modulus, Z = b*h^2 / 6 = 83333 mm^3
Moment of inertia, I = b*h^3 / 12 = 4166667 mm^4
Max. pressure, Pmax = 24.97 kPa
Max. force on one joist, q = Pmax*S = 7.492 kN/m
For simply support,
Maximum span, L = 700 mm
Check bending moment:
Max. bending moment, M = qL^2 / 8 = 0.459 kNm
Bending stress, fb = M/Z = 5.51 N/mm^2 < 7.1 N/mm^2, OK!
Check shear:
Max. shear force, V = qL/2 = 2.622 kN
Shear stress, fq = V/bh = 0.52 N/mm^2 < 1.32 N/mm^2, OK!
Check deflection:
Max. deflection, d = 5qL^4 / 384EI = 0.74 mm < L/270 = 2.593 mm, OK!
For cantilever
Maximum cantilever length, Lc = 250 mm
Check bending moment:
Max. bending moment, M = qLc^2 / 2 = 0.234 kNm
Bending stress, fb = M/Z = 2.81 N/mm^2 < 7.1 N/mm^2, OK!
Check shear:
Max. shear force, V = qLc = 1.873 kN
Shear stress, fq = V/bh = 0.37 N/mm^2 < 1.32 N/mm^2, OK!
Check deflection:
Max. deflection, d = qLc^4 / 8EI = 0.116 mm < Lc/270 = 0.926 mm, OK!
Railing check
Use 2nos. 50mm x 26mm x 1.4mm thk. steel R.H.S grade S275
Section size of one steel RHS,
B = 26 mm, D = 50 mm, t = 1.4 mm, d = 47.2 mm, b = 23.2 mm
Spacing of railing, S = 700 mm
Elastic modulus, Z = 5402.8 mm^3
Moment of inertia, I = 135070 mm^4
Maximum span, L = 600 mm
Max. force on one joist, q = 7.492 kN/m
Max. force on railing from one joist, P = q*S = 5.244 kN
Check shear:
Max. shear force, V = P*1.4 = 7.342 kN
Design strength, py = 275 N/mm^2
Shear capacity, Vc = py*4td / 3^0.5 = 41.966 kN > 7.342 kN, OK!
Check bending moment:
Max. bending moment, M = PL/4*1.4 = 1.101 kNm
Moment capacity, Mc = 1.2*py*Z = 1.783 kNm > 1.101 kNm, OK!
Check deflection:
Max. deflection, d = P*L^3 / 48EI = 0.852 mm < L/270 = 2.222 mm, OK!
Anchor bar check
Use 12mm diameter high yield steel bar in 45° with horizontal
Area of cross section, A = 12^2*3.14 / 4 = 113.10 mm^2
Spacing, Sv = 700 mm (vertical), Sh = 600 mm (horizontal)
Max. pressure, Pmax = 24.97 kPa
Max. force on steel bar, T = Pmax*Sv*Sh*1.4 / cos45° = 20.769 kN
Tensile stress, ft = T / A = 183.64 N/mm^2 < 400.2 N/mm^2, OK!
Water plate check
Section size of washer, b = 70 mm, t = 8mm
Elastic modulus, Z = b*t^2 / 6 = 747 mm^3
Max. force on anchor bar, T = 20.769 kN (factor = 1.4)
Max. bending moment, M = T*23 / 2 = 0.239 kNm
Design Strength, py = 275 N/mm^2
Moment capacity, Mc = 1.2*py*z = 0.246 kNm > 0.239 kNm, OK!
Reference
a) BS:5975:1996 Code of practice for falsework
b) Code of practice for the structural use of steel 2011
c) Steel designers manual - 5th edition
d) Formwork - a guide to good practice
Design data and assumption
a) Plywood : 18mm thk. Birch-faced
Bending stiffness, EI = 3.02 kNm^2/m
Moment of resistance, fZ = 0.655 kNm/m
Shear load, qA = 10.534 kN/m
b) Joist : 50mm x 100mm timber @300mm c/c grade SC3
Permissible bending stress, Pb = 7.1 N/mm^2
Permissible compressive stress, Pc = 2.63 N/mm^2
Permissible shear stress, Pq = 1.32 N/mm^2
Modulus of elasticity, E = 7600 N/mm^2
c) Railing : 2nos. 50mm x 26mm x 1.4mm thk. steel R.H.S grade S275
Design strength, py = 275 N/mm^2
Modulus of elasticity, E = 205000 N/mm^2
d) Anchor : Y12 steel bar Grade 460
Tensile stress, Pt = 0.87 x 460 = 400 N/mm^2
Shear stress, Pq = 0.6 x 460 = 276 N/mm^2
e) Washer : 8mm thk. steel plate grade S275
Tensile stress, py = 275 N/mm^2
Modulus of elastricity, E = 205000 N/mm^2
Concrete pressure estimation
The maximum concrete pressure on formwork is given by:
Pmax = D*[C1*R^0.5 + C2*K*(H - C1*R^0.5)^0.5]
where:
C1 = coefficient dependent on the size and shape of formwork
C2 = coefficient dependent on the constituent materials of the concrete
D = weight density of concrete
H = vertical form height
K = temperature coefficient taken as [36 / (T + 16)]^2
R = the rate at which the concrete rises vertically up the form
T = concrete temperature at placing
example case,
C1 = 1.0, C2 = 0.3, D = 24, H = 4.0, K = 0.612, R = 0.5, T = 30
C1*R^0.5 = 0.707 m (< H = 4.0m)
Pmax = 24 x [1 x 0.5^0.5 + 0.3 x 0.612 x (4 - 1 x 0.5^0.5)^0.5] = 24.97 kPa
Plywood check
Thickness of plywood, t = 18mm
Width of backing beam, B = 50mm
Maximum span, L = 300 mm
Max. pressure, Pmax = 24.97 kPa
Max. force on one span sheathing, W = Pmax*L = 7.492 kN/m
Max. bending moment, M = 0.095WL = 0.214 kNm/m < 0.655 kNm/m, OK!
Check shear:
Max. shear force, V = 0.525W(L-B-T)/L = 3.042 kN/m < 10.534 kN/m, OK!
Check deflection:
Max. deflection, d = 0.0066WL^3/EI = 0.442 mm < L/270 = 1.11 mm, OK!
Joist check
Section size of timber joist, b = 50 mm, h = 100 mm
Spacing, S = 300 mm
Elastic modulus, Z = b*h^2 / 6 = 83333 mm^3
Moment of inertia, I = b*h^3 / 12 = 4166667 mm^4
Max. pressure, Pmax = 24.97 kPa
Max. force on one joist, q = Pmax*S = 7.492 kN/m
Maximum span, L = 700 mm
Check bending moment:
Max. bending moment, M = qL^2 / 8 = 0.459 kNm
Bending stress, fb = M/Z = 5.51 N/mm^2 < 7.1 N/mm^2, OK!
Check shear:
Max. shear force, V = qL/2 = 2.622 kN
Shear stress, fq = V/bh = 0.52 N/mm^2 < 1.32 N/mm^2, OK!
Check deflection:
Max. deflection, d = 5qL^4 / 384EI = 0.74 mm < L/270 = 2.593 mm, OK!
For cantilever
Maximum cantilever length, Lc = 250 mm
Check bending moment:
Max. bending moment, M = qLc^2 / 2 = 0.234 kNm
Bending stress, fb = M/Z = 2.81 N/mm^2 < 7.1 N/mm^2, OK!
Check shear:
Max. shear force, V = qLc = 1.873 kN
Shear stress, fq = V/bh = 0.37 N/mm^2 < 1.32 N/mm^2, OK!
Check deflection:
Max. deflection, d = qLc^4 / 8EI = 0.116 mm < Lc/270 = 0.926 mm, OK!
Railing check
Use 2nos. 50mm x 26mm x 1.4mm thk. steel R.H.S grade S275
Section size of one steel RHS,
B = 26 mm, D = 50 mm, t = 1.4 mm, d = 47.2 mm, b = 23.2 mm
Spacing of railing, S = 700 mm
Elastic modulus, Z = 5402.8 mm^3
Moment of inertia, I = 135070 mm^4
Maximum span, L = 600 mm
Max. force on one joist, q = 7.492 kN/m
Max. force on railing from one joist, P = q*S = 5.244 kN
Max. shear force, V = P*1.4 = 7.342 kN
Design strength, py = 275 N/mm^2
Shear capacity, Vc = py*4td / 3^0.5 = 41.966 kN > 7.342 kN, OK!
Check bending moment:
Max. bending moment, M = PL/4*1.4 = 1.101 kNm
Moment capacity, Mc = 1.2*py*Z = 1.783 kNm > 1.101 kNm, OK!
Check deflection:
Max. deflection, d = P*L^3 / 48EI = 0.852 mm < L/270 = 2.222 mm, OK!
Anchor bar check
Use 12mm diameter high yield steel bar in 45° with horizontal
Area of cross section, A = 12^2*3.14 / 4 = 113.10 mm^2
Spacing, Sv = 700 mm (vertical), Sh = 600 mm (horizontal)
Max. pressure, Pmax = 24.97 kPa
Max. force on steel bar, T = Pmax*Sv*Sh*1.4 / cos45° = 20.769 kN
Tensile stress, ft = T / A = 183.64 N/mm^2 < 400.2 N/mm^2, OK!
Water plate check
Elastic modulus, Z = b*t^2 / 6 = 747 mm^3
Max. force on anchor bar, T = 20.769 kN (factor = 1.4)
Max. bending moment, M = T*23 / 2 = 0.239 kNm
Design Strength, py = 275 N/mm^2
Moment capacity, Mc = 1.2*py*z = 0.246 kNm > 0.239 kNm, OK!