Question

In: Civil Engineering

A specimen of concrete column (200 x 200 mm) of 1.5 m long with 4 steel...

A specimen of concrete column (200 x 200 mm) of 1.5 m long with 4 steel rebars (20 mm in diameter) inside with same length. If Ec = 21 Gpa, Es = 210 GPa, and free shrinkage strain = 0.0004, estimate the force carried by concrete and steel after shrinkage. If concrete tensile strength, ft = 5 MPa, will crack develop in this specimen?

Solutions

Expert Solution

Size of specimen = 200 * 200mm

Length = 1.5 m

20mm dia 4nos steel bars

Ec = 21GPa; Es = 210 GPa

Free shrinkage strain = 0.0004

Shortened length of pure concrete column for free shrinkage :

In equilibrium state

Shrinkage strain of steel bar :

Shrinkage strain of concrete under restraint of steel:

From equilibrium equation :

F_c = F_s

As = pi/4*D² *4 = pi*D² = 1256.64mm2

Ac = a²- pi*D² = 38743.4mm2

21*1000*(0.6-x/1500)*38743.4 = 210*1000*(x/1500)*1256.64

Therefore x = 0.453 mm

Hence after shrinkage, force carried by concrete:

Fc = 21*1000*(0.6- 0.453/1500)*38743.4 = 79.7 KN

Force carried by steel:

Fs = 210*1000*(x/1500)*1256.64 = 79.69 KN

Now:

Since load carried by concrete = 80 KN

80/.02^2 = 2000 KN/m² = 2MPa

This is less than 5 MPa, hence cracks will not develop

Ally Wells answered 1 year ago

Next > < Previous

Related Solutions

Design a square concrete column footing to support a 500-mm x 500-mm reinforced concrete column. The...

Design a square concrete column footing to support a 500-mm x 500-mm reinforced concrete column. The center of the column and footing must coincide. Loads: ???=350 ??, ???=480 ??, ???=100 ??−?, ???=130 ??−? Column Design Criteria: ??′=28 ???, ??=400??? Footing Design Criteria: ??′=28 ???, ??=400???, ??=175 ???,??=1.50 ?, ??=16 ??/?3,??=24 ??/?3, ??=20 ??, assume a thickness of the footing of 500 mm.

Design a square concrete column footing to support a 400-mm x 400-mm reinforced concrete column. The...

Design a square concrete column footing to support a 400-mm x 400-mm reinforced concrete column. The center of the column and footing must coincide. Loads: ???=350 ??, ???=480 ??, ???=100 ??−?, ???=130 ??−? Column Design Criteria: ??′=28 ???, ??=400??? Footing Design Criteria: ??′=28 ???, ??=400???, ??=180 ???,??=1.70 ?, ??=16 ??/?3,??=24 ??/?3, ??=25 ??, assume a thickness of the footing of 700 mm.

A column with 7 m high and 397 mm X 488 mm masonry is built with...

A column with 7 m high and 397 mm X 488 mm masonry is built with 25.8 Mpa CMUs in M mortar, with four vertical bars, Fy = 414 MPa, placed in grout with the same strength of the CMUs. The column is designed to carry 1000 KN axial compression forces. a) Find the minimum steel reinforcement and the bars diameters As min = 0.0025 Ag, 0.0025 An < As < .04 An b) Calculate the allowable axial load Pa=(0.25fm'An+0.65...

A steel alloy specimen having a rectangular cross section of dimensions 19.1 mm × 3.0 mm...

A steel alloy specimen having a rectangular cross section of dimensions 19.1 mm × 3.0 mm (0.7520 in. × 0.1181 in.) has the stress-strain behavior shown in the Animated Figure 6.22. If this specimen is subjected to a tensile force of 95120 N (21380 lbf) then (a) Determine the amount of elastic strain induced. (b) Determine the amount of plastic strain induced. (c) If its original length is 590 mm, what will be its final length after this force is...

A pipe, 900 m long and 200 mm in diameter discharges water to the atmosphere at...

A pipe, 900 m long and 200 mm in diameter discharges water to the atmosphere at a point 10 m below the inlet level. With an inlet pressure of 40 kPa gauge, the flow rate is 40 litres/sec. At a point half way between the pipe inlet and outlet, a new tapping is made from which water is taken at a rate of 18 litres/sec. To what value must the inlet pressure be raised in order to maintain the same...

Plot the head loss in a 500 m long 200 mm cast iron pipe for the...

Plot the head loss in a 500 m long 200 mm cast iron pipe for the following flow rates; 0.001, 0.01, 0.1, and 1 m3/s. Use (a) the Moody Diagram and (b) the Swamee-Jain equation to find the friction factor and (c) the Hazen-Williams Eq. Discuss why the losses are similar or different for parts a and c

In a galvanised steel water supply line 100 m long and 50 mm in diameter, water...

In a galvanised steel water supply line 100 m long and 50 mm in diameter, water is pumped from a reservoir to a vented storage tank at an elevation 8 m above it. The following fittings are use: 1 hinged foot valve with strainer, 3 x 90? elbows, 2 gate calves (open), 20 screwed sockets, 1 sudden exit. The water viscosity is 1 x 10-6 m2/s and the density is 1000 kg/m3. (a) Calculate the friction factor at a flow...

At what distance ‘X’ will the carbon concentration in a steel specimen be 0.70 wt. %...

At what distance ‘X’ will the carbon concentration in a steel specimen be 0.70 wt. % after 10h at 1100 0C, if the starting composition was 0.35 wt. % C and the surface concentration is 1.35 wt.% C? how do you get x/2sqrt(DT)=0.66085?

Please answer the question: A 24 inch diameter spirally reinforced concrete column with a 1.5 inch...

Please answer the question: A 24 inch diameter spirally reinforced concrete column with a 1.5 inch cover to the spiral is reinforced with Grade 60 bars and has a concrete compressive strength of 5,000 psi. Determine the required diameter and pitch of the spiral reinforcement.

The column has dimension of 500 mm x 500 mm and carries an axial load of...

The column has dimension of 500 mm x 500 mm and carries an axial load of 1210 KN dead load and 650 KN live load. Allowable soil pressure is 240 Kpa. There is 0.7 m height of soil having a unit weight of 15.74 KN/m3, fc’ = 20.7 Mpa, fy = 276.5 Mpa. The footing section is 2.8 m x 2.8 m with a 600 mm thickness. Use 25 mm diameter main bars.

Subjects