Problem
Given the following elements of a circular curve: middle ordinate = 2 m; length of long chord = 70 m. Find its degree of curve, use arc basis.
Problem
The angle of intersection of a circular curve is 36° 30'. Compute the radius if the external distance is 12.02 m.
Problem
The angle of intersection of a circular curve is 45° 30' and its radius is 198.17 m. PC is at Sta. 0 + 700. Compute the right angle offset from Sta. 0 + 736.58 on the curve to tangent through PC.
Vertical Parabolic Curve
Vertical curves are used to provide gradual change between two adjacent vertical grade lines. The curve used to connect the two adjacent grades is parabola. Parabola offers smooth transition because its second derivative is constant. For a downward parabola with vertex at the origin, the standard equation is
Spirals are used to overcome the abrupt change in curvature and superelevation that occurs between tangent and circular curve. The spiral curve is used to gradually change the curvature and superelevation of the road, thus called transition curve.
Compound Curves
A compound curve consists of two (or more) circular curves between two main tangents joined at point of compound curve (PCC). Curve at PC is designated as 1 (R1, L1, T1, etc) and curve at PT is designated as 2 (R2, L2, T2, etc).
Formulas for Circular Curves
The formulas we are about to present need not be memorized. All we need is geometry plus names of all elements in simple curve. Note that we are only dealing with circular arc, it is in our great advantage if we deal it at geometry level rather than memorize these formulas.
Fundamentals of Surveying
Tape Measurements
Leveling
Angles and Directions
Transits and Theodolites
Traverse
Highway Curves
Topographic Surveys
Control Surveys
Construction Surveys
Hydrographic Surveys
Land Surveys
Photogrammetry
Problem
A propped beam 8 m long is to support a total load of 28.8 kN/m. It is desired to find the steel reinforcements at the most critical section in bending. The cross section of the concrete beam is 400 mm by 600 mm with an effective cover of 60 mm for the reinforcements. f’c = 21 MPa, fs = 140 MPa, n = 9. Determine the required number of 32 mm ø tension bars and the required number of 32 mm ø compression bars.
Problem
A reinforced concrete cantilever beam 4 m long has a cross-sectional dimensions of 400 mm by 750 mm. The steel reinforcement has an effective depth of 685 mm. The beam is to support a superimposed load of 29.05 kN/m including its own weight. Use f’c = 21 MPa, fs = 165 MPa, and n = 9. Determine the required number of 28 mm ø reinforcing bars using Working Stress Design method.
