PAST EXAMINATION PAPERS – Numerical Problems with Answers
module: - Temporary Works
Academic Year 2007/08
Q.1 Fig. Q1 shows a 7.4 m tall cantilever formwork designed for casting successive lifts of concrete 4 m each in height. The formwork has a steel truss strongback behind the plywood sheeting and is anchored by three rows of anchor bolts at 1.0 m vertically apart as shown in the figure. It weighs 20 kN per longitudinal metre run. The horizontal spacing for each row of anchor bolts is 0.5 m center to center. Anticipated site conditions during concreting operation will be as follows:
Concrete temperature 5° – 32°C
Unit weight of concrete 25 kN/m3
Rate of concrete delivery Each 4-m lift will be completed in 8 hours.
(a) Given the following formula in computing concrete pressure acting on formwork, determine the design concrete pressure in kPa for the 4-m LIFT and draw the concrete pressure distribution diagram accordingly.
Hint: in kPa, or
(6 marks)
(Ans. 77.67 kPa)
(b) Among the three horizontal rows of anchor bolts, it is assumed that the middle bolts are installed for additional safety only and will not offer any tension nor compressive forces under normal design condition. Calculate the tension in each upper anchor bolt in kN for the formwork having a safety factor of 1.2 against overturning about its lower row of anchor bolts.
(12 marks)
(Ans. 255.025 kN)
(c) Calculate the tension in each anchor bolt in the middle row if all the anchor bolts of the uppermost row fail in pull-out mode.
(4 marks)
(Ans. 510.049 kN)
(d) State the general considerations in structural design of falsework
(3 marks)
Q.2 Fig. Q2 shows the elevation layout of a typical transverse row of a birdcage scaffold structure measured 8.4 m (H) and 9.1 m (W). There are 12 rows of falsework framework in longitudinal direction each comprising of mild steel tubing and fittings all complying with BS1139. The falsework will be erected to support the construction of a concrete slab.
Given the following configuration of the falsework and design loading information:
Design LoadingConcrete slab thickness / 150 mm
Operation load / 2.0 kPa
Self weight of Formwork & Scaffolding / 1.0 kPa
Design wind speed / 40 m/s
Falsework Configuration
Lift Height / 1.4 m
Bay Length / l 1.30 m c/c in transverse direction
l 1.35 m c/c in longitudinal direction
Solidity Ratio of scaffolding exposed to transverse wind: / 5%
(a) Determine the total wind moment acting on the falsework structure. Assume that the dynamic wind pressure q (in KPa) for wind speed Vd (in m/s) is given by and pressure coefficient Cf = 1.3 and 2.0 for circular scaffolding tubing and the edge form respectively. (5 marks)
(Ans. 27.643 kN-m per row)
(b) Determine the total leg load in kN in each individual verticals (standards) of the scaffold under the combined vertical and horizontal loading condition. Using the Table Q2 to check the axial loading capacity of the verticals against lateral buckling. Identify if there are any verticals under tension. Assume scaffolding tubes of “USED” condition will be used.
(13 marks)
(Ans.13.11 kN; None of the Verticals are under Tension)
(c) Determine the minimum number of diagonal braces required to resist the horizontal wind load. Draw the layout of the diagonal braces provided for the falsework.
(4 marks)
(Ans. Two (2) Diagonal Braces per row)
(d) Determine the safety factor against overturning for the falsework when the soffit formwork is standing EMPTY but with operation load and calculate the kentledge required, if required, to meet the minimum safety factor of 1.2
(3 marks)
(Ans. 6.07; No Kentledge is req’d)
Hint: Formulas for calculating leg loads induced by overturning moment M are given as follows:
Q.3 A large panel of soffit formwork is designed for the construction of a 250 mm thick concrete deck slab.
Determine the maximum spacing of the formwork components given the following design and formwork material information are used.
Design Information
Unit weight of concrete - 25 kN/m3
Construction operation load – 2.0 kN/m2
Deflection not to exceed 1/360 of span
Formwork Material Information
Formwork Materials
/ Permissible Moment of Resistance / Permissible Shear Load / StiffnessEI
Plywood Sheeting / 0.420 kN-m /m / 7.86 kN /m / 3.50 kN-m2 /m
Timber Bearers each 3 metres long / 1.00 kN-m / 6.80 kN / 79.14 kN-m2
Steel Joists supported by vertical props / 5.39 kN-m / 30.21 kN / 100.58 kN-m2
Hint: Assume all formwork components are continuous beams of multiple equal spans and the following formulas to be used.
Max. Bending Moment for a continuous beam under UDL
@
Max. Shear Force @
Max. Deflection d = 0.007 for plywood; and
d = 0.004 for bearers and steel joists,
where ω = Uniformly Distributed Load (UDL) on span L (kN per metre run)
(25 marks)
(Ans. Timber Bearer - 0.550 m c/c; Steel Joist - 1.475 m c/c; Prop - 1.75 m c/c)
Q.4 A propped cantilever steel sheet piling cofferdam is designed to resist a 6 m (H) high vertical cut as detailed in Fig. Q4. Given the following soil properties and loading information :
Active earth pressure coefficient Ka 0.30
Passive earth pressure coefficient Kp 2.85
Unit weight of soil 18 kN/m3
Surcharge Load 20 kN/m2
and the net earth pressure diagram shown in the figure, use the free earth support method to determine the:
(i) Depth of point of zero net earth pressure (Z);
(4 marks)
(Ans. 0.84 m)
(ii) Prop load if the props are spaced to leave a working clearance of 3.0 m on plan for equipment passing between the ground level and the bottom of excavation;
(12 marks)
(Ans. 248.81 kN)
(iii) Minimum depth of embedment (D) that the pile has to be driven if the factor of safety for moment equilibrium is designed to be not less than 2.0. (Hint start D=X+Z = 2.8 m for iterations).
(5 marks)
(Ans.3.16 m)
(iv) Suggest with illustration alternative design provision if there are existing underground utilities which obstruct the depth of piling to be driven as obtained in (iii)
(4 marks)
Academic Year 2006/07
Q.1 Fig. Q1 shows the elevation layout of a typical transverse row of a birdcage scaffold structure measured 7.8 m (H) and 8.4 m (W). The framework consists of mild steel tubing and fittings all complying with BS1139. The longitudinal spacing of scaffold is at 1.35 m center to center. It is designed to support an elevated working platform with an operation load of 1.5 kPa. The combined selfweight of the falsework and platform is 1.0 kN per m2 of plan area. The design transverse wind speed Vd in the vicinity of the structure is 20 m/s. Assume the platform structure is equipped with a toe board 0.2 m high along its free edges at the roof level.
(e) Verify that the total wind moment acting on the whole scaffold structure is 8.37 kN-m per row. Assume that the dynamic wind pressure is given by (Vd in ms-1 and q in kPa) and pressure coefficient Cf = 1.3 and 2.0 for circular scaffolding tubing and the edge toeboard respectively. Assume that the solidity ratio of the scaffold area exposed to the transverse wind is 6%.
(5 marks)
(Ans. 8.371 kN-m per row)
(f) Determine the total leg load in kN in each individual verticals (standards) of the scaffold under the combined vertical and wind loading condition. Using Table Q1, check the axial loading capacity of the verticals against lateral buckling if they are all of “Used” condition. Identify if there are any verticals under tension.
(10 marks)
(Ans. 4.47 kN, None of Verticals are under tension)
(g) Determine the minimum number of diagonal braces required to resist the horizontal wind load. Draw the layout of the diagonal braces provided for the scaffold structure.
(7 marks)
(Ans. One (1) Diagonal Brace per row)
(h) Determine the safety factor against overturning for the scaffold structure if there is no construction activity on the platform and calculate the kentledge required if it is less than 1.2.
(3 marks)
(Ans. 5.69 No Kentledge is required)
Q.2 A formwork is proposed for concreting a 800x800 square column. The design internal concrete pressure of 90 kN/m2 is to be resisted by the components given in the table as shown underneath. Using the formulae on Page 7 and the following design loading/criteria information and formwork material properties:
(a) Calculate the maximum spacing of individual formwork components to the nearest 25 mm;
(20 marks)
(b) Prepare the typical column formwork layout.
(5 marks)
Design Loading/Criteria
Concrete pressure 90 kN/m2
Deflection 1/360 of span of each formwork
component.
Material Properties
Formwork Materials / Permissible Moment of Resistance / Permissible Shear Load / StiffnessEI
Plywood Sheeting
(per m width) / 0.420 kN-m /m / 9.952 kN /m / 3.50 kN-m2 /m
Vertical 50x225 Timber Studs each 2.5 m long / 2.500 kN-m / 8.93 kN / 73.00 kN-m2
Horizontal 50x127 RSJ Waler / 12.057 kN-m / 50.67 kN / 496.44 kN-m2
(Ans. Vertical Stud – 0.175 m c/c; Horizontal Waler – 0.925 m c/c; Toe Rod – 1.025 m c/c)
Q.4 The 5 metres high single skin cantilever wall form detailed in Fig. Q4 is designed to receive concrete mix from its top in one go. The rate of vertical rise of concrete level will reduce gradually from 450 mm per hour at the bottom to 150 mm per hour at the top of the wall form throughout the concrete filling process.
Anticipated site conditions during concreting will be as follows:
Concrete temperature 10° – 35°C
Unit weight of concrete 25 kN/m3
(a) Given the following formula in computing concrete pressure acting on formwork, determine the design concrete pressure in kPa for the form in every 1-m intervals and hence plot its variation along the height of the form.
in kPa, or
(20 marks)
(Ans.
Depth / Rate of Rise / Pmax by Formula / Hydrostatic D*h / Design Pressure / Elev. above bottomh / R
m / m/h / kN/m2 / kN/m2 / kN/m2 / m
0.00 / 0.150 / 56.00 / 0.00 / 0.00 / 5.00
1.00 / 0.210 / 57.42 / 25.00 / 25.00 / 4.00
2.00 / 0.270 / 58.64 / 50.00 / 50.00 / 3.00
3.00 / 0.330 / 59.73 / 75.00 / 59.73 / 2.00
4.00 / 0.390 / 60.73 / 100.00 / 60.73 / 1.00
5.00 / 0.450 / 61.65 / 125.00 / 61.65 / 0.00
(b) Assume the maximum concrete pressure Pmax calculated from part (a) is UNIFORMLY ACTING on the full height of the wall form and there are two parallel rows of external raking struts erected at a horizontal spacing of 0.8 m centre to centre to support the concrete pressure thrust as shown in the Fig. Q4. If a minimum factor of safety of 1.5 against strut failure is to be adopted, what is the design axial load in each individual strut assuming that they are all equally loaded ?
(5 marks)
(Ans. 261.54 kN)
Q.6 A single-propped cantilever steel sheet piling cofferdam is designed to resist a 4.5 m high vertical cut as shown in Fig.Q6. Given the following soil properties and design information:
Height of soil to be retained 4.5m
Depth of the prop below ground level 0.6 m
Horizontal spacing of props 3 m
Active Earth Pressure Coefficient Ka 0.25
Passive Earth Pressure Coefficient Kp 2.00
Unit weight of soil 17 kN/m3
Surcharge Load 20kN/m2
Use FREE EARTH SUPPORT METHOD to determine the:
(i) Depth of point of zero net earth pressure Z (4 marks)
(Ans. 0.811 m)
(ii) Determine the strut load (12 marks)
(Ans. 132.12 kN)
(iii) Minimum depth of embedment D that the pile has to be driven.
(Ans. 2.81 m )
(9 marks)
(Hint: Try the depth below point of zero net earth pressure X = 1.0 m for the first iteration )
Academic Year 2005/06
Q.1 An illegally constructed concrete slab measuring 6 m long and 1.2 m wide and of thickness 250 mm standing 2.6 m above a footpath was found defective and ordered to be removed by the Buildings Department. A contractor is subsequently called upon to remove the slab while the pedestrian traffic underneath has to be maintained. For executing the demolition work, the Contractor proposes to use steel beams at the ceiling which in turn are supported by a shore structure assembled from BS 1139 steel scaffolding tubing and fittings to protect pedestrians under the ceiling as shown in Fig.Q1. Given the following design information:
Imposed load 2.0 kPa
Steel Beam 1.5 kPa
Self weight of Scaffolding Frame 0.5 kPa
Unit weight of Concrete 24 kN/m3
Lateral Load designed to be 2.5% of total vertical load applied at the ceiling level
(i) Verify that the overturning moment acting on a typical interior transverse row of shore structure above the footpath level is 1.17 kN-m;
(5 marks)
(Ans. 1.17 kN-m per row)
(ii) Use the overturning moment of 1.17 kN-m to calculate the maximum scaffold leg load and check its structural adequacy from Table Q1; (Assume scaffolding is of “USED” condition)
(5 marks)
(Ans. 9.975 kN)
(iii) Determine the factor of safety against overturning for the typical transverse row;
(5 marks)
(Ans. 9.23)
(iv) Determine the number of diagonal bracing required for the longitudinal stability of the scaffold shore structure and draw the layout arrangement. Assume couplers of 6.5 kN capacity each are used to fix diagonal braces.
(10 marks)
(Ans. One (1) Longitudinal Diagonal Brace)
Q.2 Fig. Q2 shows the layout of a formwork for a 1000x1000 square column. The formwork consists of an internal plywood sheeting lining supported around its periphery by vertical studs each 1.35 m long at 200 mm centre to centre. The internal design concrete pressure of 80 kN/m2 is resisted by two opposite walers at 1400 mm apart which are in turn tied together at their ends with a pair of steel tie rods. The horizontal walers spacing is 450 mm centre to centre. Use the formulae on Page 7 and the following design loading/criteria information and formwork material properties to check the adequacy of the formwork layout. If any component of the layout is found unsatisfactory, suggest improvement measure(s).