在香港，用木材(timber and plywood)作模板固定落石屎是最常使用的，因為廉價和方便。但用於牆身模板時，一般高度達2米以上，就需要斜撐或拉固(inclined support or tie)，這樣，我們如何檢查模板能否安全企穩呢? 以下是我驗算的方式 :
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
Review of stability of formwork
Design concrete pressure, Pa = 24.97 kPa
Rate of concrete rise, Up = 0.5 m/hr (assumed)
Equivalent initial setting time, Ti = 24.97 / (0.5 x 24) = 2.08 hr (say 2.5 hr)
Height of concrete without initial setting, H = 2.5 x 0.5 = 1.25 m
Height of concrete pressure, H1 = 24.97 / 24 = 1.04 m
Height of concrete pressure, H2 = 1.25 - 1.04 = 0.21 m (H - H1)
1) Check initial stage of concreting (without concrete setting)
Weight of bottom bar, Wb = 0.097 kN/m of each T40
Spacing of bottom bar, Sb = 0.15 m for B1 and B2
Total weight of bottom bar, Wbt = 0.097 / 0.15 x 2 x (10.0 / 2) = 6.467 kN/m
Restoring moment due to steel bar, Wt = 6.467 x 5.0 / 2 = 16.167 kNm/m
Overturning moment (about O) = 12.98 x (0.21 + 1.04 / 3) + 5.24 x 0.21 / 2 = 7.776 kNm
Factor of safety, FOS = 16.167 / 6.467 = 2.50 > 2.0, OK!
2) Check final stage of concreting (with concrete setting at lower portion)
Design concrete pressure, Pa = 24.97 kPa
Rate of concrete rise, Up = 0.5 m/hr (assumed)
Equivalent initial setting time, Ti = 24.97 / (0.5 x 24) = 2.08 hr (say 2.5 hr)
Height of concrete with initial setting = 4.0 - 1.25 = 2.75 m
Weight of concrete = 24 kN/m^3 x 2.75 x (10.0 / 2) = 330 kN/m (ignored weight of steel bottom bar)
Restoring moment due to steel bar, Wt = 330 x 5.0 / 2 = 825 kNm/m
Concrete lateral force, F1 = 24.97 x 1.04 / 2 = 12.98 kN/m
Concrete lateral force, F2 = 24.97 x 0.21 = 5.24 kN/m
Overturning moment (about O) = 12.98 x (4.0 - 1.04 x 2 / 3) + 5.24 x (0.21 / 2 + 2.75) = 57.881 kNm/m
Factor of safety, FOS = 825 / 57.881 = 14.253 > 2.0, OK!
Obviously, stability of formwork is critical before concrete setting at lower portion.
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
Review of stability of formwork
Design concrete pressure, Pa = 24.97 kPa
Rate of concrete rise, Up = 0.5 m/hr (assumed)
Equivalent initial setting time, Ti = 24.97 / (0.5 x 24) = 2.08 hr (say 2.5 hr)
Height of concrete without initial setting, H = 2.5 x 0.5 = 1.25 m
Height of concrete pressure, H1 = 24.97 / 24 = 1.04 m
Height of concrete pressure, H2 = 1.25 - 1.04 = 0.21 m (H - H1)
1) Check initial stage of concreting (without concrete setting)
Weight of bottom bar, Wb = 0.097 kN/m of each T40
Spacing of bottom bar, Sb = 0.15 m for B1 and B2
Total weight of bottom bar, Wbt = 0.097 / 0.15 x 2 x (10.0 / 2) = 6.467 kN/m
Restoring moment due to steel bar, Wt = 6.467 x 5.0 / 2 = 16.167 kNm/m
Overturning moment (about O) = 12.98 x (0.21 + 1.04 / 3) + 5.24 x 0.21 / 2 = 7.776 kNm
Factor of safety, FOS = 16.167 / 6.467 = 2.50 > 2.0, OK!
2) Check final stage of concreting (with concrete setting at lower portion)
Design concrete pressure, Pa = 24.97 kPa
Rate of concrete rise, Up = 0.5 m/hr (assumed)
Equivalent initial setting time, Ti = 24.97 / (0.5 x 24) = 2.08 hr (say 2.5 hr)
Height of concrete with initial setting = 4.0 - 1.25 = 2.75 m
Weight of concrete = 24 kN/m^3 x 2.75 x (10.0 / 2) = 330 kN/m (ignored weight of steel bottom bar)
Restoring moment due to steel bar, Wt = 330 x 5.0 / 2 = 825 kNm/m
Concrete lateral force, F1 = 24.97 x 1.04 / 2 = 12.98 kN/m
Concrete lateral force, F2 = 24.97 x 0.21 = 5.24 kN/m
Overturning moment (about O) = 12.98 x (4.0 - 1.04 x 2 / 3) + 5.24 x (0.21 / 2 + 2.75) = 57.881 kNm/m
Factor of safety, FOS = 825 / 57.881 = 14.253 > 2.0, OK!
Obviously, stability of formwork is critical before concrete setting at lower portion.