Mechanics of Solids ( Final exam question)

[civilnerd11]

hello all!
I am new to this forum. I am doing Mechanic of Solid ( summer course). I have come across with this problem , but I don't know how to solve it. I have attached the question. Could anyone help me?
I don't know how to convert from density to force. in this questions
given are

weight of concrete= 25 kN/m^3
Height of the water contained by the dam= 3.3 m
density of water= 1000 kg/m^3
Stresses at A and B=?

In order to find out stresss, I need to know forces. This is where I get stuck!
Thank you very much!

 

[gsal]

You have density of water (mass per cubic meter) and gravity, and so you can calculate the weight (F=ma) of a column of water all the way to the bottom of the dam.

 

[civilnerd11]

Here is my workout for this problem. But I need to find stresses at Point A and B. I guess I take a moment at either A or B and find the forces. But stress= Force/area. Area is not given in this problem. How do I go from here? Thanks!

1) weight of the dam W= mg= pvg= (pg)v= rV= 25 kN/m^3 ( 2.16 X 3.6 /2 X b) pg= weight density, b= width= 97.2 b kN

2) Resultant hydrostatic force of water= density of water X gravity X height= 1000 kg/m^3 X 9.8 m/s^2 X 3.3 m- 32.373 kPa therefore weight b= 32.373kN Magnitude of the resultant force F= 32.373 b kN X 3.3 / 2 = 53.42 kN

I am stuck here again. Could anyone help me? Thank you so much!1

 

[AlephZero]

It doesn't matter how long the dam is. The stress won't change along the length. So if you want to do the math "properly" take the length as L and it will cancel out eventually. Or if you just want to get to the answer, assume the dam is 1 meter long.

I can't help you on how to find the stresses, because the answer depends on making some assumptions about how the dam is fixed to the ground, but that is not included in the question. Maybe civil engineers are supposed to "know" what those assumptions are, but I don't.

 

[DeeNos]

Hello and welcome to the forum! I can understand your confusion with this problem. In order to solve this, we need to use the concept of pressure. Pressure is defined as force per unit area, and can be calculated by dividing the force by the area it is acting on. In this case, we are dealing with a dam, where the force is the weight of the water and the area is the base of the dam.

To convert from density to force, we need to use the formula: Force = Density x Volume x Gravity. In this case, the volume is the area of the base of the dam multiplied by the height of the water. So, we can calculate the force acting on the dam by multiplying the density of water (1000 kg/m^3) by the volume (3.3 m^3) and gravity (9.8 m/s^2). This gives us a force of 32,340 N.

Now, to find the stresses at points A and B, we need to divide this force by the area of the base of the dam. This will give us the pressure acting on the dam, which can then be converted to stresses by using the formula: Stress = Pressure x Depth. We can assume that the depth at points A and B is the same, so the stress at these points will be equal.

I hope this helps you solve the problem. Good luck on your exam!