This set of Irrigation Engineering Multiple Choice Questions & Answers (MCQs) focuses on “Arch Dams – Design”.
1. Which of the following forces is the least important in the design of arch dams?
a) Reservoir water force
b) Uplift pressure
c) Temperature stresses
d) Ice load
Explanation: The uplift pressure in an arch dam is generally neglected because it is small due to the narrow base width of its body. Ice load, Temperature stresses and yield stresses are quite important in such dams and are thoroughly examined.
2. Which of the following theory is the most accurate method to design arch?
a) The thin cylinder theory
b) The theory of elastic arches
c) The trial load method
d) Creep theory
Explanation: Thin cylinder theory can only be relied upon for rough estimation of dimensions of the arches. The Elastic theory does not take into account the thickness of arch rings and the restrictions at the abutments. The Trial load method removes the above objections and leads to an accurate estimation of the stresses in arches.
3. Which among the following is not an assumption of the ‘Trial Load Analysis’ method of design of arch dams?
a) Plane sections normal to the axis remain plane after flexure
b) Any horizontal arch ring is independent of the arch rings below and above
c) Modulus of elasticity of concrete and rock foundation is equal for compression and tension
d) Stresses are proportional to strains
Explanation: In Trial load method, the dam is divided into two systems of elements i.e. the horizontal arches and the vertical cantilevers. Each element is supposed to take a percentage of the load due to silt and water pressure. The actual distribution of the load between these elements is then arrived at by several trials.
4. The thin cylinder theory for designing arch dams is based only on ___________________
a) temperature stresses
b) ice pressures
c) yield stresses
d) hydrostatic water pressure
Explanation: In thin cylinder theory analysis, the design is based only on hydrostatic water pressure. The theory does not take into account the shear and bending stresses in the arch, temperature stresses, and ice pressures which are quite important in arch dams.
5. The temperature stresses producing worst effects in the design of arch dams are caused by ______________
a) rise in temperature
b) fall in temperature
c) both rise and fall
d) no effect in the design
Explanation: The dam moves upstream during the summer and downstream during the winter due to the internal stresses caused by the temperature changes. In stress analysis, the low temperature becomes quite important since these stresses act additive to the reservoir water pressure.
6. The stresses due to rib-shortening become quite important in the case of _____________
a) long thin arch dams
b) thick arch dams of small angle
c) both thin and thick arch dams
d) all types of arch dams
Explanation: In the case of an arch dam, the ends being fixed the distance between them does not change and this restriction of the change in the span causes additional stresses known as rib-shortening stresses. These stresses are small in a long thin arch but in the case of a thick arch of small-angle, they are appreciable.
7. Which of the following is not the basis for the design of an arch dam?
a) Thin cylinder theory
b) Trial load theory
c) Unit column theory
d) Elastic theory
Explanation: Arch dams are designed on the basis of any one of the following three methods–
• Thin cylinder theory
• Theory of Elastic arches
• Trial load method
Out of these methods, the trial load method is generally adopted nowadays and it gives precise results.
8. According to thin cylinder theory, the volume of concrete required for an arch dam would be minimum if the central angle is ____________
a) 130° 34’
b) 133° 34’
c) 143° 34’
d) 153° 34’
Explanation: The most economical central angle is equal to 133°-34’ and such an angle can be adopted only at one place in constant radius arch dam as there is considerable variation with height due to narrow V-shape of the valley. It is therefore considered to keep the economical angle of 133°-34’ at about mid-height for a minimum value of concrete.
9. The best design of an arch dam is when __________________
a) all horizontal water loads are transferred horizontally to the abutments
b) the dam is safe against sliding at various levels
c) the load is divided between the arches and cantilevers and the deflections at the conjugal points being equal
d) the deflections of the cantilevers are equal at different points
Explanation: In the trial load method, deflections for the arches are calculated at the points where the cantilevers cross it in each trial. If the deflection calculated at these points from cantilever elements is within reasonable limits and same, then the assumed distribution of load is correct. If not, then the calculations are repeated using a different set of load distribution until the condition is satisfied.
10. At a given elevation, the thickness of the arch ring is proportional to the radius of the arch.
Explanation: The thickness of the arch ring (t) under limits is given by –
t = ϒw . h. r / fc where r is the radius of the arch, h is depth, fc is the allowable compressive stress for the arch material and ϒw is the unit weight of water.
It is clear from the above equation that the thickness of the arch is proportional to the radius of the arch at a given elevation.
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