Mixing Concrete and Concrete Beams - Day 1 - Questions

1. The 8 in by 8 in concrete beam section shown below was tested in a third point loading apparatus. The failure occurred outside the middle third as shown under a maximum total load of 5000lbf. The beam was normal weight concrete with compressive strength of 5000psi. Neglect the beam’s self weight.

a) Find the maximum shear force.
b) Find the maximum bending moment
c) Find the shear force within the middle third.
d) Find the shape of the moment within the middle third
e) Find the modulus of rupture
f) If the fracture had happened in the middle third, find the modulus of rupture.
g) Use the ACI empirical equation to find the modulus of rupture.
h) If the beam is made of lightweight concrete, what is the modulus of rupture?


2. A normal weight concrete structure tested at 28 days yields the following:
a) An 8 in by 10 in concrete cylinder failed in axial compression at 110,000 lbf. Find the ultimate compressive strength.
b) An 8 in by 10 in concrete cylinder resisted a transverse force of 50,000 lbf in a split cylinder test, find the tensile strength.
c) An 8 in square unreinforced beam section resisted a force of 5500 lbs on a 24 in span length. A third point loading test was used and the fracture occurred within the middle third. Find the modulus of rupture.
d) Find the ratio of the modulus of rupture to the compressive strength
e) Find the ratio of the split tensile strength to the compressive strength
f) Given a compressive strength of 3800 lbf/in^2 find the modulus of rupture.
g) Axial strain is 0.0016 in/in and lateral strain is 0.00028 in/in. Find Poission’s ratio.

3. A trial batch of concrete is needed according to the following requirements:

# of sacks of cement per yd^3 of concrete = 8
Entrained air – 5%
Total water-cement ratio = 0.55
Cement specific gravity = 3.20

For economical reasons, 2 sizes of coarse aggregate were used. The aggregates are as follows:
SG Moisture % by volume
Fine aggregate 2.55 5% excess 35%
¾ in coarse 2.60 2% excess 17%
1.0 in coarse 2.57 3% deficit 48%

a) find the weight of cement needed for 2 yd^3 of concrete
b) find the volume of cement needed for 2 yd^3 of concrete
c) find the weight of water needed for 2 yd^3 of concrete
d) find the volume of water needed for 2 yd^3 of concrete
e) The absolute volume of fine aggregate in 2 yd^3
f) The SSD weight of fine aggregate in 2 yd^3
g) The absolute volume of ¾ in aggregate in 2 yd^3
h) The absolute volume of 1.0 in aggregate in 2 yd^3
i) The SSD weight of ¾ in aggregate in 2 yd^3
j) The SSD weight of 1.0 in aggregate in 2 yd^3

Mixing Concrete and Concrete Beams - Day 1

Chapters 48 and 49 in Lindeburg



Chapter 48 - Properties of Concrete and Reinforcing Steel - 5 Problems

Chpater 49 - Concrete Proportioning, Mixing, and Placing - 3 Problems

Traffic and Accident Analysis - Answers

I marked these pages:

Headway, Spacing, Volume - Section 10 - Page 74-6

Warrants for signal - Section 16 - Page 74-14

I also downloaded some info from the HCM 2000 - in the form of class notes regarding the designs for 2 lane highways and multiland highways - I didn't feel like the info in the book was enough, especially since the answers to the questions kept referencing HCM.

Today's Answers:

Traffic and Accident Analysis - Questions

I am studying the material in Chapter 74, but the questions require the use of HCM, which I do not currently have, so I am not able to post questions, since I’m am unsure I will be able to answer them.

For Chapter 75 though – I present these 2:

1. Two cars are moving at 50 mph in the same directions in the same lane. The cars are separated by 20 ft per 10 mph. The coefficient of friction (skidding) is 0.65. The reaction time is assumed to be 0.4 sec.
a) If the lead car hits a parked car, what is the speed of the second car when it hits the first car?
b) If the lead car hits a parked car and comes to an abrupt halt, at what speed does the rule of 1 car length (20 ft) per 10 mph of speed become unsafe?
c) At 60 mph what should the rule actually be?

2. Two vehicles collide head on while traveling a curve with a 4% grade. Vehicle A skidded 200 feet downhill before colliding with vehicle B. Vehcile B skidded 150 ft. The police report estimates both car traveling at 30 mph prior to the collision. Assume a coefficient of friction of 0.5.
a) What was the speed of vehicle A prior to hitting the brakes?
b) What was the speed of vehicle B prior to hitting the brakes?
c) Which assumption produces the greatest possible error?

Traffic and Accident Analysis

Chapters 74 and 75 in Lindeburg



Chapter 74 - Roads and Highways : Capacity Analysis - 6 Problems

Chapter 75 - Vehicle Dynamics and Accident Analysis - 4 Problems

Highway Curves - Answers

I marked these pages:

Stopping Sight Distance - Table 79.2 - Page 79-10

Today's Answers:

Highway Curves - Questions

1. Use the following diagram:

a) At what station is the low point located?
b) At what elevation is the low point?
c) At what elevation is the sta 21+75.05
d) What is the highest design speed for the curve?
e) What is the rate of grade change per station?
f) If 18 ft of clearance is required, what is the lowest elevation that the bottom of an overhead bredige deck may have at sta 22+75

2. The grades on a vertical curve intersect at station 110+00 and elevation 352 ft. A drain grating exists at sta 110+00 at elevation 360.25 ft

a) Given a curve length of 1800 ft, what is the elevation of BVC?
b) Given a curve length of 1800 ft, what is the elevation of sta 111+40?
c) Given a curve length of 1800 ft, what is the elevation of the low point?
d) Given a curve length of 1800 ft, what is the station of BVC?
e) Given a curve length of 1800 ft, what is the elevation of EVC?

3.
The tangent of the horizontal curve shown is relocated 12 ft west of its original position. The PC remains the same.
a) What is the original curve radius?
b) What is the new curve radius?