Stocky Columns

Question 1

What is the definition of a column?

Answer 1

h is no greater than 4b

Question 2

What is biaxial bending?

Answer 2

Bending moments from 2 directions

Question 3

What is uniaxial bending?

Answer 3

Bending in one direction

Question 4

What does no moment mean?

Answer 4

No bending in any direction.

Question 5

If we have a bending moment - axial load graph, and are given load and bending moment are located within the curve, what does this mean?

Answer 5

It is a safe combination.

Question 6

If we have a bending moment - axial load graph, and our given load and bending moment are located on the line of the curve, what does this mean?

Answer 6

Either compressive or tension failure, if below the balance point it is tension failure. If above the balance point, it is compression failure.

Question 7

When analysing a column and there is no axial load, what is the step by step process to calculate the design moment?

Answer 7

1 - Forces equilibrium, find the value of epsilon,sc
2 - Gain a quadratic equation for x, to find the position of the neutral axis.
3 - From this find moments about the bottom steel to calculate the design moment

Question 8

When analysing a column, the compression steel is at point of yielding, how do we find the Axial load and bending moment of this column?

Answer 8

1 - Forces equilibrium and find epsilon,sc
2 - Axial load = F,sc + F,c - F,st
3 - Bending moments about the centre line.

Question 9

When analysis a column, the section is completlely balanced, with x = 0.617d. How do we find the axial load and bending moment?

Answer 9

Axial load is equal to Sum of the compression forces - the sum of the tension forces.

Take bending moments about the centre line

Question 10

When analysing a column section to find the bending moment and axial load, it is found that the neutral axis is down to the level of the tension steel, how do you go about finding the axial load and bending moment?

Answer 10

1 - x = d
2 - Axial load = sum of the compression forces
3 - Take bending moments about the centre line (the compression forces apply only)

Question 11

When analysing a column to find the axial load and bending moment, it is found that the neutral axis is at the bottom of the section, how do you find the bending moment and axial force from this?

Answer 11

1 - Find epsilon,st to therefore find fs
2 - As bottom steel is in compression, the axial force is the sum of everything
3 - Take bending moments about centreline, but minus the moment of the force from the bottom steel this time.

Question 12

When analysing a column section in order to find the bending moment and axial force, it is found that the section fails under pure compression with no bending moment, how would you find the axial force considering there is no bending moment?

Answer 12

All strains across section = ecu / 2

Go from there

Question 13

When we wish to calculate the resistance of a section to a combination of axial load and compression, we need to know one of the values beforehand. What do we do for case (a) a given value of NEd, find the corresponding Mrd. And case (b) for a given value of Mrd, find the corresponding axial load?

Answer 13

For a given value of N,Ed, the solution will depend on whether N,Ed is above / below the balance point.

For a given value of M,Ed, we expect to find 2 values of N,Ed.

Question 14

When determining the axial load and bending moment of the balanced section, what is the process?

Answer 14

1 - Make x = 0.617d
2 - Determine N,Ed, using fyd for steel in compression and tension
3 - Check compression steel has yielded

Question 15

We are given a axial load which is less than the axial load of the balanced section, what is the step by step process to find the design moment?

Answer 15

1 - As N,Ed > N,Ed,bal the tension steel must have yielded
2 - Estimate depth of neutral axis assuming compression steel has also yielded, and find a value of x.
3 - If the compression steel has NOT yielded, recalculate depth of neutral axis assuming elastic compression of steel and get a new value for Mrd

Question 16

We are given an axial load which is greater than the axial load of the balanced section, what is the step by step process to find the design moment?

Answer 16

1 - Tension steel has not yielded. We know compression has yielded
2 - Use the value of NEd to find x, using fst instead of fyd as the tension steel has not yielded
3 - After finding x find the value of Mrd

Question 17

We are given a value of the moment resistance, and need to find the 2 values of the axial resistance. How do we go about doing this?

Answer 17

We need to consider an lower branch, where x < x,bal and a an upper branch, where x > x,bal.

For the lower branch, assume both tension and compression have reached yield and calculate x. Check compression steel has yielded, and if not recalculate again to find new value of x.

For the upper branch, use fst instead of fyd as tension has not yielded whereas compression has. Find the value of Nrd.