A plain concrete member is fixed between two

immovable abutments $($hence $=0).$ Determine:

a$)$ The short$-$term change in temperature $(T)$

required to crack the concrete in tension. Also

determine the width of the crack if $T=-40C.$

b$)$ The short$-$term change in temperature $(T)$

required to compress the concrete by $5$MPa.

c$)$ The number of days after the formwork is

removed when the concrete will crack due to

drying shrinkage. Also determine the width of

the crack if ${}_{sh}=-0\mathrm{.}4{10}^{-3}.$ For $($c$)$ ignore

creep effects and assume no change in

temperature.

Calculate and plot $($on the same graph$)$ both the

short$-$term and long$-$term axial load vs$.$ axial

deformation $(N-)$ relationships for Columns $"A"$

and $"$B$".$ Column $"$A$"$ does not have any reinforcing

bars. Use a spreadsheet and provide sample hand

calculations.

For the short$-$term case, assume that there are no

creep, shrinkage or thermal effects since the load is

applied quickly. For the long$-$term case, calculate

the expected concrete shrinkage strain, ${}_{sh,}$ and the

expected creep coefficient, $(t,t_i),18$ years after

casting. The formwork was removed one week

after casting and the loads were applied eight

weeks after casting. For both the short and long$-$

term case there is no change in temperature.

For both plots, show the complete range of values

for $N$ and $,$ indicating on the graph various

important points, including the maximum

compressive and tensile loads, concrete cracking,

concrete crushing, steel yielding, and axes

intersections $($values of $$ at $N=0,$ and values of $N$

at $=0).$ Discuss the differences between the short$-$

term and long$-$term behaviours, and the differences

between the unreinforced and reinforced members.

$f_c=30$MPa

${}_c^{\text{'}}=-0\mathrm{.}002$

Concrete made with limestone aggregate

Average $RH=70\%$