March 2017

Consistency is the term used to describe the ability of the soil to resist rupture and deformation. It is commonly describe as soft, stiff or firm, and hard.
 

Water content greatly affects the engineering behavior of fine-grained soils. In the order of increasing moisture content (see Figure 2 below), a dry soil will exist into four distinct states: from solid state, to semisolid state, to plastic state, and to liquid state. The water contents at the boundary of these states are known as Atterberg limits. Between the solid and semisolid states is shrinkage limit, between semisolid and plastic states is plastic limit, and between plastic and liquid states is liquid limit.
 

Atterberg limits, then, are water contents at critical stages of soil behavior. They, together with natural water content, are essential descriptions of fine-grained soils.
 

Consider a relatively long simply supported beam shown below. Assume the load w_o to be increasing progressively until the beam fails. The beam will go into the following three stages:

1. Uncrack Concrete Stage – at this stage, the gross section of the concrete will resist the bending which means that the beam will behave like a solid beam made entirely of concrete.
2. Crack Concrete Stage – Elastic Stress range
3. Ultimate Stress Stage – Beam Failure

Problem
A rectangular concrete beam is reinforced in tension only. The width is 300 mm and the effective depth is 600 mm. The beam carries a moment of 80 kN·m which causes a stress of 5 MPa in the extreme compression fiber of concrete. Use n = 9.
1.   What is the distance of the neutral axis from the top of the beam?
2.   Calculate the required area for steel reinforcement.
3.   Find the stress developed in the steel.
 

Problem
A reinforced concrete beam 300 mm wide has an effective depth of 600 mm. It is reinforced with 4-32 mm diameter bars for tension. f’_c = 21 MPa and f_y = 275 MPa. Find the moment capacity of the beam.
 

Problem
A 300 mm × 600 mm reinforced concrete beam section is reinforced with 4 - 28-mm-diameter tension steel at d = 536 mm and 2 - 28-mm-diameter compression steel at d' = 64 mm. The section is subjected to a bending moment of 150 kN·m. Use n = 9.

1. Find the maximum stress in concrete.
2. Determine the stress in the compression steel.
3. Calculate the stress in the tension steel.
 

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, f_s = 140 MPa, n = 9. Determine the required number of 32 mm ø tension bars and the required number of 32 mm ø compression bars.
 

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.

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.
 

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.