2080 Central Level Subjective for Civil Engineers Solution

Section – A  (30 Marks)

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1. Define simply supported and cantilever beams. Derive maximum bending moment for the beams in uniformly loaded condition. (2+8 = 10)

Answer

Simply supported beam is a type of beam supported on the ends which are free to rotate and have no moment resistance. It undergo shearing and bending.

A cantilever beam is a beam with one end fixed and other end free.

   Derivation of maximum bending moment for the beams in uniformly loaded condition

(a) Simply supported beam

Consider a simply supported beam AB of length l and carrying a uniformly distributed load of w per unit length as shown in fig.

Since the load is uniformly distributed over the entire length of beam,

By symmetry,

Reaction at A (R_A) Reaction at B (R_B)

Bending moment at any section at a distance x from A,

M_X R_A  x
  x

For maximum bending moment,

0
i.e.     0
x i.e. mid point of the beam where S.F changes sign as shown in fig.

Thus,
Maximum bending moment,
M_max      
M_max

(b) Cantilever beam

Consider a cantilever beam AB of length l and carrying a uniformly distributed load of w per unit length, over the entire beam as shown in fig.

Shear force at any section X, at a distance x from B,
F_x  wx
Thus, we see S.F is zero at B (where x 0 ) and increases by a straight line to wl at A as shown in fig.
Bending moment at X,
M_X
    (Minus sign due to hogging moment)

Thus, we see B.M is zero at B (where x 0 ) and increases in the form of a parabolic curve to at A (where x = l ) as shown in fig.

Maximum bending moment,

M_max   

2. Describe the advantages and disadvantages of prestressed concrete. (10)

Answer

Prestressed concrete is a type of concrete in which internal stresses of suitable magnitude are introduced so that the stresses resulting from external loadings can be counteracted to a desired degree.

In reinforced concrete, pre-stress is commonly introduced by tensioning the reinforcement. So, compression is induced in the zones where external load would normally cause tensile stress which is then neutralized by the pre-induced compressive stress.  Hence, the zone will be free from any stress.

Advantages 

• It is possible to take full advantage of high compressive strength of concrete and high tensile strength of steel used. The combination of two superior quality materials result in most economical section.
• Prestressed concrete can be safely used for structures having longer span such as bridges and which are subjected to heavy loads, impact and vibrations.
• Pre stressing eliminates the cracks in concrete under all stages of loading. Therefore, the entire section becomes effective unlike RCC structures where the section above neutral axis only carries the compressive stress.
• Pre stressed concrete members are comparatively smaller in section. Thus, saving of materials.
• Reduced dead weight of superstructure also saves the cost of foundation.
• There is considerable saving in cost of shuttering and centering in large structures as PSC members are mostly manufactured in factories.
• There is considerable saving in stirrups, since the shear in PSC members is reduced by inclination of tendons and the diagonal tension is further minimized by the presence of prestress.
• In PSC structures, deflection of beam is considerably reduced.

 Disadvantages 

• Pre stressed sections are more brittle because of use of high tension steel.
• Pre stressed concrete members construction requires high degree of workmanship, good quality control and supervision.
• Pre stressing requires specialized tensioning equipments and devices which are very costly.
• Cost of materials used in PSC is very high.
• Complex safety requirements.

3. What forces should we consider while designing the retaining wall to stabilize the slope during road construction in hills? Enumerate. (10)

Answer

A retaining wall is a structure designed and constructed to resist the lateral pressure of soil or other materials of two different ground levels. Retaining walls are commonly used in landscaping, road construction, and building foundations to create level surfaces on sloped terrains, prevent soil erosion and stabilize embankments.

Designing a retaining wall to stabilize slopes during road construction in hills involves considering various forces as mentioned below to ensure stability and safety:

i. Lateral Earth Pressure

The main force that acts on a retaining wall is the lateral force developed due to the earth pressure which tends to destabilize the wall by overturning, bending and sliding the wall.

The magnitude of the lateral earth pressure varies linearly with depth and is given by
p kH  (acts at a height from the base of the wall).

where, p is the lateral earth pressure which can be active or passive.

Active pressure occurs when the soil mass yields in such a way that it tends to stretch horizontally as the retaining wall moves away from the backfill. Similarly, Passive pressure exists when the movement of the wall is such that the soil tends to compress horizontally i.e. the retaining wall moves towards the backfill.

ii. Weight of the retaining wall

It is the most important force as the stability of the retaining wall largely depends on the self weight of the wall. The total weight is considered acting at the center of gravity of the wall.

iii. Surcharge Loads

Loads from any additional weight on the surface of the soil behind the wall, such as traffic loads, pedestrian pathways or other structures.

iv. Seismic Forces

Seismic waves are set up in the earth’s crust, due to earthquake which impact acceleration to the foundation and cause its movement. In order to prevent cracking, rupture or failure of wall, seismic forces in horizontal and vertical direction should be considered in design.

v. Water Pressure

Hydrostatic pressure (pressure exerted by water behind the wall) and seepage forces (resulting from water moving through the soil) should be considered as these can lead to soil erosion and instability.

vi. Wind Pressure

In structures located in high wind zones  and in case of tall retaining walls or those supporting lightweight, flexible structure, forces resulting due to wind loads should also be addressed.

vii. Temperature Changes

Thermal expansion and contraction can cause additional stresses in the wall subjected to higher temperature variation.

viii. Construction Loads

Temporary loads and forces during the construction phase whose effects are significant should also be considered.

Fig : Forces acting on retaining wall

Each of the above mentioned forces must be carefully analysed and incorporated while designing the retaining wall to ensure the stability of slope and structures in hill roads. Apart from this, proper site selection, investigations, materials quality , drainage considerations and adherence to safety factors and standards are crucial for a successful design.

Section – B  (25 Marks)

4. What is a unit hydrograph (UH) ? How do you estimate design flood using UH? Mention. (5)

Answer

Unit hydrograph is a direct runoff hydrograph resulting due to unit depth ( 1cm ) of rainfall excess occurring uniformly over an entire area with uniform intensity with a specified direction. UH is effective for basin area greater than 2 km² and smaller than 5000 km² .

Estimation of design flood using UH

i. Obtain rainfall data.

ii. Develop the unit hydrograph

iii. Calculate the ordinates of direct rainfall hydrograph
Ordinates of DRH Ordinate of UH R depth

iv. Calculate the ordinate of flood hydrograph
Ordinates of flood hydrograph Ordinate of DRH Base flow 

5. Assume that you are assigned with a responsibility of investigating a case of failure of a bridge immediately after its construction. What steps would you follow to investigate whether hydrology is a potential cause of the failure? Illustrate the steps with appropriate examples. Also, show a template of report (with notes on expected contents under different chapters/sub-chapters) of such investigation to submit to a higher authority. (7+3 = 10)

Answer

Steps I would follow to investigate whether hydrology is a potential cause of the failure

I. Initial assessment and data collection

• Site visit – Detailed inspection of bridge site to assess the visible damage and conditions.
• Historical Data – Collection of long term historical hydrological and meteorological data including rainfall, river flow, and flood records.
• Design Review – Examination of the original design documents and construction records of the bridge, focusing on hydrological considerations.

II. Hydrological Analysis

• Rainfall Analysis – Analyzation of recent and historical rainfall data to determine if any extreme weather events could have contributed to the failure.
• Runoff Calculation – Calculation of runoff considering the catchment area and its characteristics during the period leading to bridge failure 
• Flood Frequency Analysis – Perform a flood frequency analysis to estimate the probability of different flood magnitudes and their recurrence intervals.

III. Structural Analysis 

• Load Evaluation – Assess whether bridge was subjected to load beyond its design capacity
• Scour Analysis – Examine potential scour around the bridge foundations caused by high flow velocities and turbulence.
• Material Inspection – Check for material deterioration, corrosion, or other structural issues raised by hydrological conditions.

IV. Comparative Analysis 

• Benchmarking – By comparing findings with similar bridge structures that have experienced hydrological events to identify common vulnerabilities.
• Standards Compliance – To ensure that the bridge design met current hydrological and engineering standards at the time of construction.

V. Simulation and Modelling

• Hydraulic Modelling – By using software tools to model water flow and assess the impact on the bridge structure.
• Scenario Analysis – Simulating various scenarios, including worst case hydrological events, to understand potential failure mechanism.

Vi. Conclusion and Recommendations

• Identification of root cause – summarizing findings to identify whether hydrology is a primary or contributing factor to the bridge failure.
• Mitigation measures – Recommend design improvements, maintenance measures, or other measures to prevent future failures.

Template of Investigation Report

Title Page

• Title: Investigation Report on Bridge Failure
• Date:
• Submitted By:
• Submitted To:

Executive Summary

Table of Contents

A. Introduction

• Background
• Objectives of the investigation
• Scope and limitations

B. Site Inspection

• Description of the site visit
• Visual observations and photographs

C. Data Collection and Review

• Hydrological data
• Design and construction documents

D. Hydrological Analysis

• Rainfall analysis
• Runoff calculations
• Flood frequency analysis

E. Structural Analysis

• Load assessment
• Scour analysis
• Material Inspection

F. Comparative Analysis

• Benchmarking with similar structures
• Compliance with standards

G. Simulation and Modelling

• Hydraulic modeling results
• Scenario analysis

H. Conclusion

• Summary of the findings
• Identification of the root cause

I. Recommendations

• Design and maintenance improvements
• Mitigation measures

References

• List of data sources, references and standards used

Appendices

• Detailed data tables
• Additional photographs
• Calculation sheets

This structure ensures a comprehensive approach to investigating whether hydrology played a role in the bridge failure and provides a clear, organized way to present findings and recommendations.

 

6. What are the differences between a weir and a barrage? What factors govern the design of a weir or a barrage? Explain. (4+6 = 10)

 Answer     

Weirs and barrage are barriers across the river, to raise the water level on the upstream side so as to ensure a regulated continuous supply of water into a canal. 

The differences between a weir and a barrage are:

S.N.	Weir	Barrage
1.	The major part or entire ponding is achieved by a raised crest and a smaller or nil part is achieved by the shutters.	The major part or entire ponding is achieved by gates and a smaller or nil part is achieved by the raised crest.
2.	It gives more afflux and a low control upon the river flow.	It gives less afflux and a better control upon the river flow.
3.	No provision for transportation facilities.	Roadway can be constructed over it.
4.	Operation of shutters is slow, involve labour and time.	Gates are convenient to operate.
5.	Shorter construction period.	Longer construction period.
6.	Low cost of construction	High construction cost

Factors governing the design of a weir or a barrage

i. Sub surface flow – The water seeping below the structures control the hydraulic design of a weir or a barrage as it endangers the stability of the structures by causing failure either by piping or uplift.

ii. Surface flow – The surface flow influence the hydraulic design as it may cause scour, uplift due to dynamic action and hydraulic jump. These should be investigated while designing a weir or barrage. 

iii. Safe exit gradient – It should be safe for the stability of soil particles at exit.

iv. Retrogression – Due to the construction of weir or barrage, the silt carrying capacity of the river varies leading to the progressive lowering of the downstream bed level. Therefore, provision should be made for retrogression of d/s bed, during design to protect the floor from undermining.

v. High Flood Level of river at site – for the safety, HFL is required as it governs the height of the structure.

vi. Maximum flood discharge for the river at site – to design the structures to withstand the most probable flood during its design life

vii. River cross section at weir or barrage site

vii. The stage discharge curve (Rating curve) for the river at site

vii. Crest levels – Top crest to pass the design flood safely and undersluice crest to attract a deep current infront the canal head regulator.

viii. Afflux 

ix. Waterway and discharge per meter

x. Pond levels – to feed the canal with its full supply

xi. Topography – It can affect the height, length and alignment of the structures.

xii. Geology – The geological properties of the site also governs the design of the structures as this can impact foundation design, seepage control, and stability.

xiii. Economic considerations – Cost of construction, potential benefits, and impact on local economy 

xiv. Environmental factors – Impact on wildlife habitats, water quality, and downstream water availability.

As the above mentioned factors governs the design of a weir or a barrage, these should be carefully considered to design and construct weirs and barrage that are safe, efficient, sustainable, and beneficial.

Section – C  (25 Marks)

7. Why is selecting the runway length important in airport? Mention. What factors influence the length of a runway in airport design? State. (5)

Answer

Runway is a defined rectangular area on a land aerodrome prepared for the landing and take off run of aircraft along its length.

Selecting the runway length is important in airport because of following reasons:

• To ensure aircraft performance so that aircraft can achieve the required take off speed, landing distance and accelerate stop distance.
• For safety purpose in emergency situations and adverse weather conditions, reducing the risk of accidents.
• To mitigate the impacts of geological and environmental constraints.
• To accommodate various type of aircrafts and to address the future growth and expansion.
• To ensure safe, efficient and flexible airport operations.

Factors influencing the length of a runway in airport design

i. Aircraft type, weight and performance

Take off speed, landing distance and accelerate stop distance depends upon the aircraft type which affects the runway length.

ii. Altitude and temperature

Higher the altitude and temperature , higher is the runway length required and vice versa.

iii. Runway gradient

Upward sloping runway requires more length.

iv. Wind conditions

Headwind reduces the required runway length whereas tail wind increases it.

v. Regulatory requirement

Runway length must adhere to ICAO standards to ensure safe operations.

vi. Future growth and expansion

Balancing these factors is crucial in determining the appropriate runway length in airport design to ensure safe, efficient and flexible aircraft operations.

8. Describe the factors to be considered in design of pavements. Explain about CBR method of flexible pavement design. (6+4 = 10)

Answer

Pavement refers to the surface of a road provided to support the wheel loads and to transfer the load stresses through a wider area on the soil subgrade below.

Based on the structural behaviour, road pavements are generally classified into two categories namely flexible pavement and rigid pavement.

Factors to be considered in design of

(a) Flexible Pavement

i. Wheel loads of heavy vehicles or the traffic loads

Pavement should be designed to sustain the maximum wheel load that is liable to act on it. The components related to wheel load are maximum wheel load, contact pressure, equivalent single wheel load and repetition of loads. The contact pressure and vertical stresses for circular wheel load is given by
Contact Pressure, p   and vertical stress at depth z, p [1- ]  where, a is radius of loaded area.

ii. Subgrade soil

The lowest stability value of the subgrade soil at the highest possible moisture content at the site should be considered during the design.

iii. Climatic factors

The climatic factors due to change in moisture condition, frost action and variation in temperature should be considered as these has significant effect in the design and performance of bituminous pavement layers, granular layers and subgrade of flexible pavements. Pavements subjected to adverse climatic conditions require higher thickness of flexible pavement structures.

iv. Pavement component materials in different layers

The stress distribution characteristics through the granular pavement component layers depend on characteristics of the materials used in these layers. The type of aggregates used, their shape factors and gradation along with the properties such as grade, ductility, softening point, viscosity, flash and fire point etc. of bituminous materials should be considered in design.

v. Drainage and environmental factors

Effective pavement drainage along with environmental factors such as water table, depth of cutting, embankment levels etc. that affect the drainage characteristics and performance of the pavement should be taken into account at the design and construction stages of the pavements.

vi. Design life

(b) Rigid Pavement

i. Wheel load

The components related to wheel load are maximum wheel load, contact pressure, relative location of the loading on cement concrete slab and repetition of loads.

ii. Temperature Variations

The variation in temperature causes difference in temperature between the top and bottom of the CC pavement slab which results in warping of slab and consequent development of flexural stresses. So, the temperature variations should be considered in design.

iii. Types of joints and their spacing

Longitudinal joints and transverse joints (expansion joints, contraction joints & construction joints) along with their spacing should be considered while designing rigid pavements as the width and length of CC slab depends upon longitudinal and transverse joints respectively.

iv. Subgrade and the other supporting layers below the cement concrete pavement slab

v. Drainage characteristics

vi. Design life

Thus, the above mentioned factors should be considered in design of pavements to meet the functional requirements of road users and structural requirements of highway engineer.

CBR method of flexible pavement design

The California Bearing Ratio (CBR) test is a method for evaluating the strength of subgrade soil and other pavement materials for the design and construction of flexible pavements. The test denotes a measure of resistance to penetration of a soil or flexible pavement material, of standard plunger under controlled test conditions.

The basic principle in CBR test is by causing a cylindrical plunger of 50 mm diameter to penetrate into the sample at a rate of 1.25 mm per minute. The loads required for 2.5 mm and 5.0 mm penetration of the plunger into the soil/material tested are recorded. The CBR value of the material tested is expressed as a percentage of standard load value in a standard material.

Pavement Design

• Evaluation of subgrade by conducting CBR test and determining CBR value.
• Determination of traffic load in terms of equivalent standard axle loads (ESALs) wrt design life.
• Determination of thickness of each pavement layer using design charts.

 

9. What are the design criteria for designing a rigid pavement in a highway construction? Elucidate. Specify the conditions where rigid pavement is applicable. (10)

Answer

Rigid pavements are those which possess noteworthy flexural strength or flexural rigidity and are generally made of Portland cement concrete.

The design criteria for designing a rigid pavement in a highway construction is based on Westergaard’s analysis as mentioned below:

A. Design Parameters

i. Design load and life

Design axle load is determined considering 98^th percentile  axle load and design life of normally 30 years.

ii. Temperature differential

Flexural stresses are developed due to temperature differential which causes warping of slab. To minimize its effect, the pattern of warping and its magnitude at different locations, such as interior, edge and corner of pavement slab should be determined.

iii. Width of the slabs

The slab width is the spacing between longitudinal joints.

iv. Spacing of contraction joints

The length of the slab depends on the spacing between the contraction joints and is designed considering the allowable stress in cement concrete during initial period of curing and the interface friction factor.

v. Modulus of subgrade, K

The modulus of subgrade reaction, k is determined by carrying out plate load test and is proportional to displacement.

vi. Radius of relative stiffness

Subgrade offers certain degree of resistance to slab deflection whose radius (in cm) is given by l []^1/4 where, h is slab thickness and E is modulus of elasticity of cement concrete in kg/cm².

vii. Properties of pavement quality concrete

B. Design Approach

i. Load stress

The dual wheel loads of single and tandem axles are assumed to be placed just touching the longitudinal edge of the pavement and load stresses are analyzed. The placement of wheel load just above the contraction joint without dowel bar and expansion joint with dowel bar system are also considered in analysis.

ii. Determination of edge load stress

Edge stresses due to design load is determined using charts prepared and published by IRC.

iii. Design of slab thickness considering fatigue analysis

Effects due to repetition of loads and temperature differential are considered and for safe design trial pavement thickness is assumed such the design load causes a stress ratio of 0.44 or slightly less. The axle loads causing stress ratio exceeding 0.44 are taken into account in the fatigue analysis.

iv. Determination of warping stress

Edge warping stress due to the maximum temperature differential for the assumed pavement thickness is determined.

 v. Total stress due to maximum axle load and warping

For safe design, the total flexural stress due to the highest axle load and warping should be less than the flexural strength of concrete. Else, higher pavement thickness is assumed and the trial is repeated until the total flexural stress is less than the flexural strength of concrete.

vi. Final pavement thickness is checked for corner load stress

vii. Design of dowel bar system at the expansion joints and tie bars along the longitudinal joints

Rigid Pavements due to their strength, durability and performance characteristics are applicable in following specified conditions:

• Heavy traffic loads – Areas with heavy traffic volumes and heavy loads such as highways, major urban roads and airport runways.
• High axle loads – Areas where the road is subjected to high axle loads such as industrial areas, freight terminals etc.
• No economic constraints
• Areas with poor soil conditions
• For long design life with minimal maintenance
• High temperature regions and regions with high seasonal temperature variations
• Areas where fuel or chemical spills are common such as gas stations, trucks stops etc.
• Areas requiring high surface reflectivity
• Environmental considerations where sustainable constructions practices are prioritized

Section – D  (20 Marks)

10. Draw a schematic diagram of gravity flow water supply scheme and explain the function of each parts. (5)

Answer

      Gravity flow water supply is that system in which water flows under gravity without use of any external energy to convey water from source to public stand post/tap/consumers. Gravity flow water supply systems are the most popular and widespread water supply technology in the mid hills of Nepal. 

The schematic diagram of gravity flow water supply scheme with the function of each part is explained below: 

Intake – Structure constructed at water source to draw water from source and conveys it to other components of w/s system.

Transmission Main – Conduit or pipe laid to convey water from source.

Sedimentation Tank – Provided at or near by intake site to collect water from one or more sources.

Interruption Chamber – Chamber or tank located in transmission main to break the excessive internal water pressure build in the pipeline.

Reservoir – to store water

Distribution System – network of pipeline to convey the water from the reservoir to the consumer premises.

Break Pressure Chamber – located in distribution system to break the excessive internal water pressure build in the pipeline. It is provided with a float valve inside.

Public Stand Post/Tap – structure in the pipeline from where water is distributed to the consumers.

Valves and fittings – for specific purpose

 

11. Ideally, water supply system should run for 24 hours and 365 days a year. This system is known as Continuous Water Supply System (CWS). But because of various reasons, many cities supply water few hours of a day or even per week. This system is called Intermittent Water Supply System (IWS). There is an agreement that CWS system is better than IWS in terms of network’s durability and maintaining the water quality. Why the network’s durability and water quality are compromised in IWS? Explain the reasons. (5)

Answer

The network and water quality issues in IWS are frequent pressure fluctuations, air entrainment, corrosion and scaling, contamination risk, biofilm formation and sediment resuspension, all of which can lead to leaks and pipe bursts. Even though CWS mitigate these issues by maintaining a continuous supply of water, IWS is provided with compromising the network’s durability and water quality because of following reasons:

1. Scarcity of water exists- IWS is provided when there is insufficient water resources to fulfill the water demand of the consumers.
2. Inadequate infrastructure to supply water continuously
3. For easy repair and maintenance works
4. Unplanned expansion of distribution network results in interrupted flow
5. In case of distribution system having weaker joints and excessive leakage, restrained supply hours can limit the leakage

Increasing access to piped water in low income and developing countries combined with many factors means that IWS will remain a common practice even though it threaten the drinking water supply system.

12. Point out the sources of water supply in Nepal. Describe the standard of drinking water quality prescribed by WHO. Also, clarify the processes for treatment of water. (2+4+4 = 10)

Answer

The sources of water supply in Nepal are broadly classified into surface sources and subsurface or ground sources as pointed below:

Surface sources – Rivers, Streams, Lakes, Ponds and Impounded Reservoirs

Subsurface sources – Springs, Wells, Infiltration galleries and Infiltration wells

The World Health Organization (WHO) sets the water quality standard to ensure that water consumed is safe, clean and free from pathogens. The standard of drinking water quality prescribed by WHO is described below:

Parameters	Unit	Maximum concentration limits set by WHO
pH		6.5 – 8.5
Turbidity	NTU	5
Color	TCU	5
Taste and Odour		would not be objectionable
Iron	mg/l	0.3
Manganese	mg/l	0.1
Arsenic	mg/l	0.01
Fluoride	mg/l	1.5
Ammonia	mg/l	1.5
Chloride	mg/l	250
Sulphate	mg/l	250
Copper	mg/l	2
Calcium	mg/l	25
Potassium	mg/l	12
Total hardness	mg/l	500
Total alkalinity	mg/l	500
E coli	CFU/100 ml	0

WHO guidelines serves as a basis for national water quality standards and these standards emphasize the importance of comprehensive water quality management from source to consumer, ensuring safety throughout the entire water supply system.

Clarification processes for treatment of water

Water treatment is a process of making the water suitable for the intended purpose by removing the impurities present in water.

The treatment process should be selected depending on the type and concentration of impurities to be removed from water as mentioned:

Treatment Process and Removal of Impurities

Screening – Large suspended and floating material

Plain Sedimentation – Coarse and heavy suspended particles

Sedimentation with Coagulation – Fine suspended particles and colloidal matters

Filtration – Very fine suspended and colloidal impurities, micro-organisms

Dis-infection – Pathogenic micro-organisms

Softening – Hardness

Aeration – Color, odour and taste, iron & manganese

Removal of Iron and Manganese – Iron & Manganese

Removal of color, odour and taste – Color, odour & taste

Fig: Schematic layout of the water treatment plant