Discuss the concept of concrete maturity meters.

$150 \mathrm{~mm} \times 300 \mathrm{~mm}$ concrete cylinders were made of the same batch and separated at random to six equal groups. The six groups of cylinders were submerged in water for different times before testing for compressive strength and the results are shown in table. It is required to do the following: a. Determine the compressive strength at different curing times. b. Using an Excel sheet, plot the relationship between curing time and compressive strength. Label all axes and curves. c. Comment on the effect of curing time on the compressive strength. d. What is the approximate ratio between the compressive strengths at 7 days and 28 days? e. What is the approximate ratio between the compressive strengths at 28 days and 180 days?

$$\begin{array}{|l|c|c|c|c|c|c|} \hline \text { Group no. } & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \text { Water submergence (days) } & 3 & 7 & 14 & 28 & 90 & 180 \\ \hline \begin{array}{l} \text { Average maximum load before } \\ \text { failure }(\mathrm{kN}) \end{array} & 189.6 & 379.1 & 543.5 & 632.0 & 733.0 & 789.9 \\ \hline \end{array}$$

Three batches of concrete were prepared using the same materials and ingredients, except that they have water-cement ratios of $0.50,0.55$, and $0.60$ , respectively. The following tests were performed on specimens made of the three batches:

• Compressive strength test on $4^{\prime \prime} \times 8^{\prime \prime}$ cylinders
• Center-point flexure test on $4^{\prime \prime} \times 4^{\prime \prime} \times 12^{\prime \prime}$ beams
• Split tension test on $6^{\prime \prime} \times 12^{\prime \prime}$ cylinders Three replicates were tested for each test. Table shows the average failure loads for the three replicates of each case. It is required to do the following: a. Complete table. b. Using an Excel sheet, plot the relationships between water-cement ratio and compressive strength, modulus of rupture, and tensile strength on the same graph. Label all axes and curves. c. Comment on the effect of water-cement ratio on the compressive strength, modulus of rupture, and tensile strength.

A normal-weight concrete has an average compressive strength of $20 \mathrm{~MPa}$. What is the estimated flexure strength?

Three batches of concrete were prepared using the same materials and ingredients, except that they have water-cement ratios of $0.50,0.55$, and $0.60$ , respectively. The following tests were performed on specimens made of the three batches:

• Compressive strength test on $100 \mathrm{~mm} \times 200 \mathrm{~mm}$ cylinders
• Center-point flexure test on $100 \mathrm{~mm} \times 100 \mathrm{~mm} \times 300 \mathrm{~mm}$ beams
• Split tension test on $150 \mathrm{~mm} \times 300 \mathrm{~mm}$ cylinders Three replicates were tested for each test. Table shows the average failure loads for the three replicates of each case. It is required to do the following: a. Complete table. b. Using an Excel sheet, plot the relationships between water-cement ratio and compressive strength, modulus of rupture, and tensile strength on the same graph. Label all axes and curves. c. Comment on the effect of water-cement ratio on the compressive strength, modulus of rupture, and tensile strength.

A center-point loading flexural test was performed on a concrete beam with a cross section of $4 \mathrm{~in} . \times 4$ in. and a span of $8 \mathrm{~in}$. If the failure load was $6032 \mathrm{~lb}$, find the flexure strength

A center-point loading flexural test was performed on a concrete beam with a cross section of $100 \mathrm{~mm} \times 100 \mathrm{~mm}$ and a span of $200 \mathrm{~mm}$. If the failure load was $26.9 \mathrm~{kN}$, determine the flexure strength.

Consider a standard flexural strength specimen of length $L$, width $a$, and depth $a$. Assume third point loading where the load at failure from the test machine is $P$, which is distributed evenly ( $1 / 2$ to each) over the two loading points. Derive the equation for calculating the modulus of rupture of the beam in terms of $P, L$, and $a$.

What are the advantages of using a third-point loading flexure test over a center-point loading flexure test? Draw a shear force diagram and a bending moment diagram for each case to support your answer.

What is the purpose of performing the flexure test on concrete? How are the results of this test related to the compressive strength test results?

To estimate the effect of a certain admixture on the flexure strength of concrete, two mixes were prepared, one without admixture and one with admixture. Three beams were prepared of each mix. All the beams had a cross section of $4 \mathrm{~in} . \times 4 \mathrm{~in}$. and a span of $12 \mathrm{~in}$. The third-point loading flexure strength test was performed on each beam after $7$ days of curing. The loads at failure of the beams without admixture were $6044,5071$ , and $5934 \mathrm{~lb}$, while the loads at failure of beams with admixture were $7299,73054$ , and $6983$ . find: a. The modulus of rupture of each beam in psi. b. The average moduli of rupture of the beams without and with admixture. c. The percent of increase of the average modulus of rupture due to adding the admixture.

A short plain concrete column with dimensions of $12 ~in$. $\times 12$ $in$. $\times 36$ $in$. is to be constructed. If the compressive strength of the concrete is $5000 \mathrm{~psi}$, what is the maximum load that can be applied to this column using a factor of safety of $1.2$ ?

To estimate the effect of a certain admixture on the flexure strength of concrete, two mixes were prepared, one without admixture and one with admixture. Three beams were prepared of each mix. All the beams had a cross section of $0.15 \mathrm{~m}$ by $0.15 \mathrm{~m}$ and a span of $0.45 \mathrm{~m}$. The third-point loading flexure strength test was performed on each beam after 7 days of curing. The loads at failure of the beams without admixture were $32.8,34.5$, and $31.7 \mathrm{~kN}$, while the loads at failure of beams with admixture were $39.4,35.6$, and $35.0$ kN. find: a. The modulus of rupture of each beam in MPa. b. The average moduli of rupture of the beams without and with admixture. c. The percent of increase of the average modulus of rupture due to adding the admixture.

A project specifies a concrete strength of at least $3000 ~psi$. Materials engineers will design the mix for a strength higher than that. estimate the required average compressive strength of the mix design if the standard deviation is $s=350$ $psi$. calculate the modulus of elasticity of the concrete at the required average compressive strength (the estimated strength, not the given strength).