Civil and Environmental Engineering Answers

5. What are the advantages of assigning the central pier and the abutment as fixed piers?

6. Sometimes the side of concrete bridges is observed to turn black in colour. What is the reason for this phenomenon?

The support B in the overhanging beam shown in Figure 11.24 sinks by 1 mm. If El = 300000 kNm*, determine the prop reaction.  

The free end ofa cantilever is supported by a 10 mm diametre steel wire. Determine the force in wire and maximum bending moment in the beam when the cantilever is subjected to a uniformly distributed load of intensity 40 kN/m over its entire length (Figure 11.25). Given, flexural rigidity of beam = 1 x 10" Nmm®*, Young's Modulus of the steel wire = 2 « 10° Nimm*.  

Redefine each piecewise function into the Heaviside function and find its Laplace transform.

𝑓(𝑡) ቄ

1, 0 ≤ 𝑡 < 5;

𝑒

−(𝑡−2), 𝑡 ≥ 5.

Redefine each piecewise function into the Heaviside function and find its Laplace transform.

𝑓(𝑡) ൝

1, 0 ≤ 𝑡 < 1;

4, 1 ≤ 𝑡 < 2

0, 𝑡 ≥ 2

Redefine each piecewise function into the Heaviside function and find its Laplace transform.

1. 𝑓(𝑡) ൝

0, 0 ≤ 𝑡 < 2;

2, 2 ≤ 𝑡 < 3

3, 𝑡 ≥ 3

4. Convert the following azimuths to equivalent bearings.

a. AZIMs of Line CD = 270°00’

b. AZIMn of Line DE = 228°15’

c. AZIMs of Line EF = 135°00’

5. A field is in the form of a regular pentagon. If the true bearing of side AB is N 30°30’E, determine the true azimuth from south of the following sides of the field: AB, BC, and CD. Assume that the corners of the field are labeled in a clockwise direction.

a. Determine the interior Angles.

b. Determine the true bearing and true azimuth of Side AB.

c. Determine the true bearing and true azimuth of Side BC.

d. Determine the true bearing and true azimuth of Side CD.

1. Compute the angles EOF and GOH from the following set of lines whose magnetic bearings

are given:

a. OE, S 15°14’ E and OF, S 36°00’ W

b. OG, N 70°15’ W and OH, S 52°05’ W

2. Compute the angle EPF from the following set of lines whose azimuths are given. AZIMn of Line PE = 219°02’ ; AZIMs of Line PF = 154°16’

3. Convert the following bearings to equivalent azimuths.

a. AB, S 50°10’ E

b. CD, S 45°50’ W

c. EF, N 66°30’ W

A weekly business magazine offers a 1-yearsubscription for $58 and a 3-year subscription for $116. If

you thought you would read the magazine for at least the next 3 years, and consider 20% as a minimum

rate of return, which way would you purchase the magazine: With three 1-year subscriptions or a single

3-year subscription?