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