Analysis Of Portal Frame

ANALYSIS OF PORTAL FRAME

INPUTS  Nodes

 Beams When both supports are pinned

When both supports are fixed

 Beam Sections For case 1, 2 & 3

For case 4

 Supports For case 1, 2 & 4

For case 3

 Beam Loads

RESULTS Max Bending Moment Elem ent

BM (kNm )

Max Shear Force Eleme nt

SF (kN)

Max Axial Force Eleme nt

AF (kN)

Roof

4-5 19-20

-203.1 -203.1

4-5 19-20

44.09 -44.09

4-5 19-20

42.18 42.18 (C)

Column s

3-4 20-21

-203.1 -203.1

1--4 20--23

-33.8 -33.8

1-2 22-13

53.94 53.94 (C)

Roof

19-20

-141.7

19-20

-36.5

4-5

32.15 (C)

Column s

20-21

-141.7

3-4

-27.57

22-23

44.38 (C)

Roof

19-20

-132.5

19-20

-34.2

4-5

48.31 (C)

Case 1

Case 2

Case 3

Deflectio n (mm)

Node 12 X : 0.00 Y: -250.51 Node 20 X: 43.71 Y : -0.23 Node 12 X : -21.13 Y: -167.13 Node 20 X: 8.02 Y : -0.19 Node 12 X : -6.26 Y:

-114.76

Case 4

Column s

20-21

-132.6

3-4

-44.1

22-23

44.96 (C)

Roof

19-20

-147

19-20

-36.81

4-5

33.1 (C)

Column s

20-21

-147

3-4

-28.46

22-23

45.1 (C)

Node 20 X: 13.36 Y : -0.19 Node 12 X : -21.43 Y: -135.84 Node 20 X: 8.74 Y : -0.13

Bending Moment, Axial Load and Shear Force Variations Over the Entire Frame  Bending Moment CASE 1:

CASE 2:

CASE 3:

CASE 4:

 Axial Load CASE 1:

CASE 2:

CASE 3:

CASE 4:

 Shear Force CASE 1:

CASE 2:

CASE 3:

CASE 4:

DISCUSSION Comparison of results among different cases: Overall Comparison  Bending moments in all cases When analyzing beam envelopes it is clear that the highest bending moment has been occurred near the joints which connect columns and roof members. Of the four cases the bending moment is highest when there is dead load only (case 1). Also we can observe a considerable reduction in bending moments when both supports are fixed.  Shear forces in all cases Of the four cases, the shear force in roof members is highest when there is dead load only (case 1), whereas in column members it is highest when supports are fixed. There is no huge change in shear force values in corresponding elements, between the different cases and the beam envelope for shear force variation has an overall common shape except slight differences.  Axial forces in all cases In most of the cases except the case 3, the highest axial force values occur at the column members. That is because the axial forces increase when the self weights of each member accumulate.

a) Case 1 and 2 When comparing the results, in case 1 & 2, it is obvious that the shear forces, axial forces and bending moments in all members have reduced in case 2 when wind is present. This is because the wind loads act in a direction opposite to the dead loads. As vertical sheets are also affected by the wind forces we can see deflection of one column is reduced in case 2 as wind force counters moment acting on it. We can see that the vertical deflection of roof has reduced in case 2 due to the wind force action perpendicular to the roof

b) Case 2 and 3 When the supports are fixed, shear forces and bending moments in members have reduced. It is clear from the beam envelopes that bending moments at supports are very high when the supports are fixed, whereas in case 2 when supports are pinned bending moment at

supports is zero. Hence the supports have to be designed carefully in case 3 to withstand that large moment. Deflection of the structure has considerably reduced when the supports are fixed.

c) Case 2 and 4 When moment resisting joints are introduced there is no any significant change in other aspects except the Y direction deflection. It is the only difference we can see in case 4 with respect to case 2. The Y direction deflection has reduced when moment resisting joints are present. It seems that deflections of the columns are not very much affected with the change in joints. Although we have used haunched moment resisting joints, there is no reasonable change in bending moments.

Advantages & disadvantages of pinned foundation joints : Pinned foundation joints are capable of accepting the resulting rotations under the design loads. Therefore the foundation needs not to be designed to resist the moments. Hence, the structure will be cost effective. The disadvantage is the deflection of the members in both directions. If this deflection is not controlled perfectly the frame will undergo considerable sway.

Advantages & disadvantages of haunched moment resisting joints Haunched moment resisting joints can withstand large bending moments without failing. They stiffen the structure. Also the deflection of the structure will be reduced. Using these types of joints is economical rather than using a larger section throughout the whole member to enhance stiffness. The disadvantage is that these type of joints need more bolting or welding which results in a higher fabrication cost.

Answers for Questions: (a) In practice, a pinned foundation joint will be introduced by bolting the column, through the welded base plate. Theoretically the bending moment in a pinned joint is zero. However, in reality it

is not possible to achieve either a purely fixed or purely pinned connection. In actual practice, the pinned joint will be able to carry a moment due to the spacing of the bolts, friction and etc. However, this moment will be comparatively small . An error will occur due to this in analysing using PROKON. As these moments are negligible, we can use it in actual practice with a safety factor .

(b) Haunches are introduced at places where there are maximum bending moments. This way the section can be kept small, hence leading to economical structure. In a portal frame haunches are introduced at the ridge (apex) and the eaves. Usually the haunch is a section cut out from a roof beam (rafter) section.

In modelling the haunch we assumed the I value of both the stanchion and the rafter to be increased by 1.5 where there is a haunch. There are two ways to model a haunch. First is to model it physically by allowing all physical changes such as area and second moment of area. Second or the more indirect method will be to model the influence of the haunch. As it is not possible to model a varying section in PROKON, we have to make changes to the structure such that the effect of having a haunch is felt, as much as possible.

Having a haunch will increase both the stiffness and the moment capacity of the joint, as well as of the surrounding area. This happens as a direct result of the change in the second moment of area of the section. As the effect of the haunch is felt by both the column and the rafter near the joint, change should be done to both. The magnitude of the change will have to be reasonable. In our case we could not observe a significant reduction in bending moments by following the above mentioned method in PROKON. Hence, I suppose that the analysis should be changed to accommodate the actual practice.