consider the pressure on a square cm due to the weight above.
Pressure= g*density*volume/area= density*height= 2.8g/cm^3 * 60m*100cm/m
then weight = pressure *(area roof in cm^2)
weight= pressure*150m*5.8m* (100cm/m)^2
check my thinking
A tunnel of length L=150m, height H=7.2m, and width w=5.8m (with a flat roof) is to be constructed at a distance d=60m beneath the ground. The tunnel roof is be entirely supported by square steel columns, each with a cross sectional area of 960 cm^2. The mass of 1.0 cm^3 of the ground material is 2.8g. a) what is the total weight of the ground material the columns must support? b) How many columns are needed to keep the compressive stress on each column at one-half of its ultimate strength?
I am not sure where to begin. Please help.
2 answers
(a) Calclate the weight of the soil above the roof. Its density is 2.8*10^3 kg/m^3. Multiply that by the roof area (5.8 m x 150 m), and the depth of the soil above (60 m). Then multiply by g to get the weight in Newtons.
(b) To do this part, you need to know the ultimate strength of the steel. You should have been given a nominal value for structural carbon steel. Set the working stress (half the ultimate stress) equal to the weight divided by the total cross section of N steel columns, and solve for N.
(b) To do this part, you need to know the ultimate strength of the steel. You should have been given a nominal value for structural carbon steel. Set the working stress (half the ultimate stress) equal to the weight divided by the total cross section of N steel columns, and solve for N.