Civil and Environmental Engineering Answers

Two concentric springs, the central spring being 5 mm shorter than the outer spring, are to be loaded as shown. The outer spring consists of 40 turns of 15 mm diameter wire coiled on a mean diameter of 100 mm. The central spring, on the other hand, has 80 turns of 20 mm diameter wire coiled on a mean diameter of 80 mm. Use 83 GPa and 76 GPa for the shear modulus of the outer and the central springs, respectively. If the load P = 2 kN, determine the stress in the central spring and the displacement of the plate.

ANALYZE AND SKETCH (SKETCHING RATIONAL FRACTIONS)

a) Y = −4/(x+1)(x^2−9)

b) Y=x^2/x^4−6x+8

find young's modulus of a rod of diameter 30mm and of length 300mm which is subjected to a tensile load of 60KN and the extension of the rod is equal to 0.4mm

Why value of uniformly distributed load w is required to produce initial cracking of the U-shaped cantilever beam shown in the figure below. The beam is constructed of normal weight concrete with f'c =25 Mpa and fy = 420Mpa.

Watch the given virtual tensile testing of material and discuss the different stages of loading the material experiences based on the result of the test

https://www.youtube.com/watch?v=cE4Mw9GsdHY&t=2s

A fireboat draws seawater SG=1.025 from submerged pipe and discharges it through a nozzle. The total head loss is 6.5ft. if the pump efficiency is 75%, what horsepower motor is required to drive it?

The brakes are set on a train running at 30 miles per hour, when ½ miles from a station. The slows down uniformly, coming to rest at the station. Find the acceleration, and the time elapsed in stopping.

solve the follow homogenous equation of differential eq (2x-3y-1)dx (x 3y-5)dy=0

Solve the homogenous equation of differential equation (x+y-2)dx+(2x-3y+1)dy=0

A.     Solve the following problems. Write your answer on a sheet of paper.

1.      Given that sin α =  and sin β = , find 𝑡𝑎𝑛 (α + β) if both α and β are in QIV.

2.      Given that csc A = , A in QI, and sec B = , sin B < 0, find

a.      cos (A – B)

b.     tan (A – B)

3.      If tan (x + y) =  and tan y = , what is tan x?

4.      The point (9, –5) lies on the terminal side of the angle 𝜃 in standard position. Find (sin 𝜃 + cos 𝜃).

B.      Solve the following problems. Write your answer on a sheet of paper.

1.      If cos t = , what is cos 2t?

2.      Use half – angle identities to find the exact value of tan 22.5⁰ and sin 15⁰.