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Challenge

Project 1

RRprasanna Venkatesh5 Aug 2023

Q 1)  The portal beam has two Bearing locations 1m from either end. The load from each bearing is 75 kN. Calculate the support reactions and displacement of each node.

Model creation in STAAD

Step 1 - Model a Portal frame with 2 portal columns of height 3 m,cross section 300mm x 300mm and Portal beam having length of 4m and cross section of 300mm x 600mm (depth)  and cross section 300mm x 300mm.

Step 2 - Provide pinned support at both columns

Step 3 - Then apply self weight for whole portal frame and 2 Live Nodal loads of 75KN at 1m from ei

ther end of the columns.

Step 4 - Save the model and run the analysis for obtaining the result given below.

Result

1. Reactions

      Horizontal Vertical Horizontal Moment
  Node L/C Fx kN Fy kN Fz kN Mx kip-in My kip-in Mz kip-in
Max Fx 3 2 LIVE LOAD 3.727 75 0 0 0 0
Min Fx 4 2 LIVE LOAD -3.727 75 0 0 0 0
Max Fy 3 2 LIVE LOAD 3.727 75 0 0 0 0
Min Fy 3 1 SELF WT 0.375 14.844 0 0 0 0
Max Fz 3 1 SELF WT 0.375 14.844 0 0 0 0
Min Fz 3 1 SELF WT 0.375 14.844 0 0 0 0
Max Mx 3 1 SELF WT 0.375 14.844 0 0 0 0
Min Mx 3 1 SELF WT 0.375 14.844 0 0 0 0
Max My 3 1 SELF WT 0.375 14.844 0 0 0 0
Min My 3 1 SELF WT 0.375 14.844 0 0 0 0
Max Mz 3 1 SELF WT 0.375 14.844 0 0 0 0
Min Mz 3 1 SELF WT 0.375 14.844 0 0 0 0

2.Displacement

      Horizontal Vertical Horizontal Resultant Rotational
  Node L/C X in Y in Z in   in rX rad rY rad rZ rad
Max X 1 2 LIVE LOAD 0 -0.005 0 0.005 0 0 -0.001
Min X 2 2 LIVE LOAD 0 -0.005 0 0.005 0 0 0.001
Max Y 3 1 SELF WT 0 0 0 0 0 0 0
Min Y 5 2 LIVE LOAD 0 -0.035 0 0.035 0 0 -0.001
Max Z 1 1 SELF WT 0 -0.001 0 0.001 0 0 0
Min Z 1 1 SELF WT 0 -0.001 0 0.001 0 0 0
Max rX 1 1 SELF WT 0 -0.001 0 0.001 0 0 0
Min rX 1 1 SELF WT 0 -0.001 0 0.001 0 0 0
Max rY 1 1 SELF WT 0 -0.001 0 0.001 0 0 0
Min rY 1 1 SELF WT 0 -0.001 0 0.001 0 0 0
Max rZ 2 2 LIVE LOAD 0 -0.005 0 0.005 0 0 0.001
Min rZ 1 2 LIVE LOAD 0 -0.005 0 0.005 0 0 -0.001
Max Rst 5 2 LIVE LOAD 0 -0.035 0 0.035 0 0 -0.001

Q 2)Now change both the supports to fixed and compare the reactions and displacements with that of previous sub question

Model creation in STAAD

Step 1 - Model a Portal frame with 2 portal columns of height 3 m,cross section 300mm x 300mm and Portal beam having length of 4m and cross section of 300mm x 600mm (depth)  and cross section 300mm x 300mm.

Step 2 - Provide Fixed support at both columns (As given)

Step 3 - Then apply self weight for whole portal frame and 2 Live Nodal loads of 75KN at 1m from either end of the columns.

Step 4 - Save the model and run the analysis for obtaining the result given below.

Result

  1. Reactions
CONDITION NODE L/C Horizontal Vertical Horizontal Moment
Fx kN Fy kN
Vertical		 Fz kN
Horizontal		 Mx kip-in
Moment		 My kip-in Mz kip-in
Q1 Q2 Q1 Q2 Q1 Q2 Q1 Q2 Q1 Q2 Q1 Q2 Q1 Q2 Q1 Q2
Max Fx 3 3 2 LIVE LOAD 2 LIVE LOAD 3.727 6.859 75 75 0 0 0 0 0 0 0 -59.773
Min Fx 4 4 2 LIVE LOAD 2 LIVE LOAD -3.727 -6.859 75 75 0 0 0 0 0 0 0 59.773
Max Fy 3 3 2 LIVE LOAD 2 LIVE LOAD 3.727 6.859 75 75 0 0 0 0 0 0 0 -59.773
Min Fy 3 3 1 SELF WT 1 SELF WT 0.375 0.69 14.844 14.844 0 0 0 0 0 0 0 -6.009
Max Fz 3 3 1 SELF WT 1 SELF WT 0.375 0.69 14.844 14.844 0 0 0 0 0 0 0 -6.009
Min Fz 3 3 1 SELF WT 1 SELF WT 0.375 0.69 14.844 14.844 0 0 0 0 0 0 0 -6.009
Max Mx 3 3 1 SELF WT 1 SELF WT 0.375 0.69 14.844 14.844 0 0 0 0 0 0 0 -6.009
Min Mx 3 3 1 SELF WT 1 SELF WT 0.375 0.69 14.844 14.844 0 0 0 0 0 0 0 -6.009
Max My 3 3 1 SELF WT 1 SELF WT 0.375 0.69 14.844 14.844 0 0 0 0 0 0 0 -6.009
Min My 3 3 1 SELF WT 1 SELF WT 0.375 0.69 14.844 14.844 0 0 0 0 0 0 0 -6.009
Max Mz 3 4 1 SELF WT 2 LIVE LOAD 0.375 -6.859 14.844 75 0 0 0 0 0 0 0 59.773
Min Mz 3 3 1 SELF WT 2 LIVE LOAD 0.375 6.859 14.844 75 0 0 0 0 0 0 0 -59.773

2.Displacement

CONDITION Node L/C Horizontal Vertical Horizontal Resultant Rotational
X in X in Y in Y in Z in Z in   in   in rX rad rX rad rY rad rY rad rZ rad rZ rad
Q1 Q2 Q1 Q2 Q1 Q2 Q1 Q2 Q1 Q2 Q1 Q2 Q1 Q2 Q1 Q2 Q1 Q2
Max X 1 1 2 LIVE LOAD 2 LIVE LOAD 0 0 -0.005 -0.005 0 0 0.005 0.005 0 0 0 0 -0.001 -0.001
Min X 2 2 2 LIVE LOAD 2 LIVE LOAD 0 0 -0.005 -0.005 0 0 0.005 0.005 0 0 0 0 0.001 0.001
Max Y 3 3 1 SELF WT 1 SELF WT 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Min Y 5 5 2 LIVE LOAD 2 LIVE LOAD 0 0 -0.035 -0.033 0 0 0.035 0.033 0 0 0 0 -0.001 -0.001
Max Z 1 1 1 SELF WT 1 SELF WT 0 0 -0.001 -0.001 0 0 0.001 0.001 0 0 0 0 0 0
Min Z 1 1 1 SELF WT 1 SELF WT 0 0 -0.001 -0.001 0 0 0.001 0.001 0 0 0 0 0 0
Max rX 1 1 1 SELF WT 1 SELF WT 0 0 -0.001 -0.001 0 0 0.001 0.001 0 0 0 0 0 0
Min rX 1 1 1 SELF WT 1 SELF WT 0 0 -0.001 -0.001 0 0 0.001 0.001 0 0 0 0 0 0
Max rY 1 1 1 SELF WT 1 SELF WT 0 0 -0.001 -0.001 0 0 0.001 0.001 0 0 0 0 0 0
Min rY 1 1 1 SELF WT 1 SELF WT 0 0 -0.001 -0.001 0 0 0.001 0.001 0 0 0 0 0 0
Max rZ 2 2 2 LIVE LOAD 2 LIVE LOAD 0 0 -0.005 -0.005 0 0 0.005 0.005 0 0 0 0 0.001 0.001
Min rZ 1 1 2 LIVE LOAD 2 LIVE LOAD 0 0 -0.005 -0.005 0 0 0.005 0.005 0 0 0 0 -0.001 -0.001
Max Rst 5 5 2 LIVE LOAD 2 LIVE LOAD 0 0 -0.035 -0.033 0 0 0.035 0.033 0 0 0 0 -0.001 -0.001

Q 3) Now provide 3 support conditions with 50 kN such that total load on the frame is same as that of Point 1. The bearings are 1m apart and 1st bearing is 1m from the end. Compare the reactions with that of sub question 2 and comment on the results.

Step 1 - Model a Portal frame with 2 portal columns of height 3 m,cross section 300mm x 300mm and Portal beam having length of 4m and cross section of 300mm x 600mm (depth)  and cross section 300mm x 300mm.

Step 2 - Provide pinned support at both columns

Step 3 - Then apply self weight for whole portal frame and 2 Live Nodal loads of 50KN at 1m from either end of the columns and one at the centre.

Step 4 - Save the model and run the analysis for obtaining the result given below.

Result

  1. Reactions
CONDITION NODE L/C Horizontal Vertical Horizontal Moment
Fx kN Fy kN
Vertical		 Fz kN
Horizontal		 Mx kip-in
Moment		 My kip-in Mz kip-in
Q2 Q3 Q2 Q3 Q2 Q3 Q2 Q3 Q2 Q3 Q2 Q3 Q2 Q3 Q2 Q3
Max Fx 3 3 2 LIVE LOAD 2 LIVE LOAD 6.859 4.141 75 75 0 0 0 0 0 0 -59.773 0
Min Fx 4 4 2 LIVE LOAD 2 LIVE LOAD -6.859 -4.141 75 75 0 0 0 0 0 0 59.773 0
Max Fy 3 4 2 LIVE LOAD 2 LIVE LOAD 6.859 -4.141 75 75 0 0 0 0 0 0 -59.773 0
Min Fy 3 3 1 SELF WT 1 SELF WT 0.69 0.375 14.844 14.844 0 0 0 0 0 0 -6.009 0
Max Fz 3 3 1 SELF WT 1 SELF WT 0.69 0.375 14.844 14.844 0 0 0 0 0 0 -6.009 0
Min Fz 3 3 1 SELF WT 1 SELF WT 0.69 0.375 14.844 14.844 0 0 0 0 0 0 -6.009 0
Max Mx 3 3 1 SELF WT 1 SELF WT 0.69 0.375 14.844 14.844 0 0 0 0 0 0 -6.009 0
Min Mx 3 3 1 SELF WT 1 SELF WT 0.69 0.375 14.844 14.844 0 0 0 0 0 0 -6.009 0
Max My 3 3 1 SELF WT 1 SELF WT 0.69 0.375 14.844 14.844 0 0 0 0 0 0 -6.009 0
Min My 3 3 1 SELF WT 1 SELF WT 0.69 0.375 14.844 14.844 0 0 0 0 0 0 -6.009 0
Max Mz 4 3 2 LIVE LOAD 1 SELF WT -6.859 0.375 75 14.844 0 0 0 0 0 0 59.773 0
Min Mz 3 3 2 LIVE LOAD 1 SELF WT 6.859 0.375 75 14.844 0 0 0 0 0 0 -59.773

0

2. Displacements

CONDITION Node L/C Horizontal Vertical Horizontal Resultant Rotational
X in X in Y in Y in Z in Z in   in   in rX rad rX rad rY rad rY rad rZ rad rZ rad
Q2 Q3 Q2 Q3 Q2 Q3 Q2 Q3 Q2 Q3 Q2 Q3 Q2 Q3 Q2 Q3 Q2 Q3
Max X 1 1 2 LIVE LOAD 2 LIVE LOAD 0 0 -0.005 -0.005 0 0 0.005 0.005 0 0 0 0 -0.001 -0.001
Min X 2 2 2 LIVE LOAD 2 LIVE LOAD 0 0 -0.005 -0.005 0 0 0.005 0.005 0 0 0 0 0.001 0.001
Max Y 3 3 1 SELF WT 1 SELF WT 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Min Y 5 7 2 LIVE LOAD 2 LIVE LOAD 0 0 -0.033 -0.052 0 0 0.033 0.052 0 0 0 0 -0.001 0
Max Z 1 1 1 SELF WT 1 SELF WT 0 0 -0.001 -0.001 0 0 0.001 0.001 0 0 0 0 0 0
Min Z 1 1 1 SELF WT 1 SELF WT 0 0 -0.001 -0.001 0 0 0.001 0.001 0 0 0 0 0 0
Max rX 1 1 1 SELF WT 1 SELF WT 0 0 -0.001 -0.001 0 0 0.001 0.001 0 0 0 0 0 0
Min rX 1 1 1 SELF WT 1 SELF WT 0 0 -0.001 -0.001 0 0 0.001 0.001 0 0 0 0 0 0
Max rY 1 1 1 SELF WT 1 SELF WT 0 0 -0.001 -0.001 0 0 0.001 0.001 0 0 0 0 0 0
Min rY 1 1 1 SELF WT 1 SELF WT 0 0 -0.001 -0.001 0 0 0.001 0.001 0 0 0 0 0 0
Max rZ 2 2 2 LIVE LOAD 2 LIVE LOAD 0 0 -0.005 -0.005 0 0 0.005 0.005 0 0 0 0 0.001 0.001
Min rZ 1 1 2 LIVE LOAD 2 LIVE LOAD 0 0 -0.005 -0.005 0 0 0.005 0.005 0 0 0 0 -0.001 -0.001
Max Rst 5 7 2 LIVE LOAD 2 LIVE LOAD 0 0 -0.033 -0.052 0 0 0.033 0.052 0 0 0 0 -0.001 0

4. Change the cross section of column to 300 x 400 mm such that 300mm width of column aligns with 300mm width of Portal beam. Rest all conditions remain same as that of sub question 2. Compare the portal beam and columns bending moment with that of sub question 2.

Step 1 - Model a Portal frame with 2 portal columns of height 3 m,cross section 300mm x 400mm such that 300mm width of column aligns with 300mm width of Portal beam and Portal beam having length of 4m and cross section of 300mm x 600mm (depth) 

Step 2 - Provide Fixed support at both columns

Step 3 - Then apply self weight for whole portal frame and 2 Live Nodal loads of 75KN at 1m from either end of the columns.

Step 4 - Save the model and run the analysis for obtaining the result given below.

Result

1.Reactions

CONDITION NODE L/C Horizontal Vertical Horizontal Moment
Fx kN Fy kN
Vertical		 Fz kN
Horizontal		 Mx kip-in
Moment		 My kip-in Mz kip-in
Q2 Q4 Q2 Q4 Q2 Q4 Q2 Q4 Q2 Q4 Q2 Q4 Q2 Q4 Q2 Q4
Max Fx 3 3 2 LIVE LOAD 2 LIVE LOAD 6.859 11.959 75 75 0 0 0 0 0 0 -59.773 -102.838
Min Fx 4 4 2 LIVE LOAD 2 LIVE LOAD -6.859 -11.959 75 75 0 0 0 0 0 0 59.773 102.838
Max Fy 3 3 2 LIVE LOAD 2 LIVE LOAD 6.859 11.959 75 75 0 0 0 0 0 0 -59.773 -102.838
Min Fy 3 3 1 SELF WT 1 SELF WT 0.69 1.202 14.844 16.964 0 0 0 0 0 0 -6.009 -10.338
Max Fz 3 3 1 SELF WT 1 SELF WT 0.69 1.202 14.844 16.964 0 0 0 0 0 0 -6.009 -10.338
Min Fz 3 3 1 SELF WT 1 SELF WT 0.69 1.202 14.844 16.964 0 0 0 0 0 0 -6.009 -10.338
Max Mx 3 3 1 SELF WT 1 SELF WT 0.69 1.202 14.844 16.964 0 0 0 0 0 0 -6.009 -10.338
Min Mx 3 3 1 SELF WT 1 SELF WT 0.69 1.202 14.844 16.964 0 0 0 0 0 0 -6.009 -10.338
Max My 3 3 1 SELF WT 1 SELF WT 0.69 1.202 14.844 16.964 0 0 0 0 0 0 -6.009 -10.338
Min My 3 3 1 SELF WT 1 SELF WT 0.69 1.202 14.844 16.964 0 0 0 0 0 0 -6.009 -10.338
Max Mz 4 4 2 LIVE LOAD 2 LIVE LOAD -6.859 -11.959 75 75 0 0 0 0 0 0 59.773 102.838
Min Mz 3 3 2 LIVE LOAD 2 LIVE LOAD 6.859 11.959 75 75 0 0 0 0 0 0 -59.773 -102.838

2.Displacements

CONDITION Node L/C Horizontal Vertical Horizontal Resultant Rotational
X in X in Y in Y in Z in Z in   in   in rX rad rX rad rY rad rY rad rZ rad rZ rad
Q2 Q4 Q2 Q4 Q2 Q4 Q2 Q4 Q2 Q4 Q2 Q4 Q2 Q4 Q2 Q4 Q2 Q4
Max X 1 1 2 LIVE LOAD 2 LIVE LOAD 0 0 -0.005 -0.003 0 0 0.005 0.003 0 0 0 0 -0.001 -0.001
Min X 2 2 2 LIVE LOAD 2 LIVE LOAD 0 0 -0.005 -0.003 0 0 0.005 0.003 0 0 0 0 0.001 0.001
Max Y 3 3 1 SELF WT 1 SELF WT 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Min Y 5 7 2 LIVE LOAD 2 LIVE LOAD 0 0 -0.033 -0.035 0 0 0.033 0.035 0 0 0 0 -0.001 0
Max Z 1 1 1 SELF WT 1 SELF WT 0 0 -0.001 -0.001 0 0 0.001 0.001 0 0 0 0 0 0
Min Z 1 1 1 SELF WT 1 SELF WT 0 0 -0.001 -0.001 0 0 0.001 0.001 0 0 0 0 0 0
Max rX 1 1 1 SELF WT 1 SELF WT 0 0 -0.001 -0.001 0 0 0.001 0.001 0 0 0 0 0 0
Min rX 1 1 1 SELF WT 1 SELF WT 0 0 -0.001 -0.001 0 0 0.001 0.001 0 0 0 0 0 0
Max rY 1 1 1 SELF WT 1 SELF WT 0 0 -0.001 -0.001 0 0 0.001 0.001 0 0 0 0 0 0
Min rY 1 1 1 SELF WT 1 SELF WT 0 0 -0.001 -0.001 0 0 0.001 0.001 0 0 0 0 0 0
Max rZ 2 2 2 LIVE LOAD 2 LIVE LOAD 0 0 -0.005 -0.003 0 0 0.005 0.003 0 0 0 0 0.001 0.001
Min rZ 1 1 2 LIVE LOAD 2 LIVE LOAD 0 0 -0.005 -0.003 0 0 0.005 0.003 0 0 0 0 -0.001 -0.001
Max Rst 5 7 2 LIVE LOAD 2 LIVE LOAD 0 0 -0.033 -0.035 0 0 0.033 0.035 0 0 0 0 -0.001 0

5. Now change the orientation of column such that 400mm size aligns with 300mm width of Portal beam. Compare the beam and column results with that of Sub question 4. Comment on the results.

Step 1 - Model a Portal frame with 2 portal columns of height 3 m,cross section 400mm x 300mm such that 400mm width of column aligns with 300mm width of Portal beam and Portal beam having length of 4m and cross section of 300mm x 600mm (depth) 

Step 2 - Provide Fixed support at both columns

Step 3 - Then apply self weight for whole portal frame and 2 Live Nodal loads of 75KN at 1m from either end of the columns.

Step 4 - Save the model and run the analysis for obtaining the result given below.

Results

1.Reactions

CONDITION NODE L/C Horizontal Vertical Horizontal Moment
Fx kN Fy kN
Vertical		 Fz kN
Horizontal		 Mx kip-in
Moment		 My kip-in Mz kip-in
Q5 Q4 Q5 Q4 Q5 Q4 Q5 Q4 Q5 Q4 Q5 Q4 Q5 Q4 Q5 Q4
Max Fx 3 3 2 LIVE LOAD 2 LIVE LOAD 8.446 11.959 75 75 0 0 0 0 0 0 -73.559 -102.838
Min Fx 4 4 2 LIVE LOAD 2 LIVE LOAD -8.446 -11.959 75 75 0 0 0 0 0 0 73.559 102.838
Max Fy 3 3 2 LIVE LOAD 2 LIVE LOAD 8.446 11.959 75 75 0 0 0 0 0 0 -73.559 -102.838
Min Fy 3 3 1 SELF WT 1 SELF WT 0.849 1.202 16.964 16.964 0 0 0 0 0 0 -7.395 -10.338
Max Fz 3 3 1 SELF WT 1 SELF WT 0.849 1.202 16.964 16.964 0 0 0 0 0 0 -7.395 -10.338
Min Fz 3 3 1 SELF WT 1 SELF WT 0.849 1.202 16.964 16.964 0 0 0 0 0 0 -7.395 -10.338
Max Mx 3 3 1 SELF WT 1 SELF WT 0.849 1.202 16.964 16.964 0 0 0 0 0 0 -7.395 -10.338
Min Mx 3 3 1 SELF WT 1 SELF WT 0.849 1.202 16.964 16.964 0 0 0 0 0 0 -7.395 -10.338
Max My 3 3 1 SELF WT 1 SELF WT 0.849 1.202 16.964 16.964 0 0 0 0 0 0 -7.395 -10.338
Min My 3 3 1 SELF WT 1 SELF WT 0.849 1.202 16.964 16.964 0 0 0 0 0 0 -7.395 -10.338
Max Mz 4 4 2 LIVE LOAD 2 LIVE LOAD -8.446 -11.959 75 75 0 0 0 0 0 0 73.559 102.838
Min Mz 3 3 2 LIVE LOAD 2 LIVE LOAD 8.446 11.959 75 75 0 0 0 0 0 0 -73.559 -102.838

2.Displacements

CONDITION Node L/C Horizontal Vertical Horizontal Resultant Rotational
X in X in Y in Y in Z in Z in   in   in rX rad rX rad rY rad rY rad rZ rad rZ rad
Q5 Q4 Q5 Q4 Q5 Q4 Q5 Q4 Q5 Q4 Q5 Q4 Q5 Q4 Q5 Q4 Q5 Q4
Max X 1 1 2 LIVE LOAD 2 LIVE LOAD 0 0 -0.003 -0.003 0 0 0.003 0.003 0 0 0 0 -0.001 -0.001
Min X 2 2 2 LIVE LOAD 2 LIVE LOAD 0 0 -0.003 -0.003 0 0 0.003 0.003 0 0 0 0 0.001 0.001
Max Y 3 3 1 SELF WT 1 SELF WT 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Min Y 7 7 2 LIVE LOAD 2 LIVE LOAD 0 0 -0.04 -0.035 0 0 0.04 0.035 0 0 0 0 0 0
Max Z 1 1 1 SELF WT 1 SELF WT 0 0 -0.001 -0.001 0 0 0.001 0.001 0 0 0 0 0 0
Min Z 1 1 1 SELF WT 1 SELF WT 0 0 -0.001 -0.001 0 0 0.001 0.001 0 0 0 0 0 0
Max rX 1 1 1 SELF WT 1 SELF WT 0 0 -0.001 -0.001 0 0 0.001 0.001 0 0 0 0 0 0
Min rX 1 1 1 SELF WT 1 SELF WT 0 0 -0.001 -0.001 0 0 0.001 0.001 0 0 0 0 0 0
Max rY 1 1 1 SELF WT 1 SELF WT 0 0 -0.001 -0.001 0 0 0.001 0.001 0 0 0 0 0 0
Min rY 1 1 1 SELF WT 1 SELF WT 0 0 -0.001 -0.001 0 0 0.001 0.001 0 0 0 0 0 0
Max rZ 2 2 2 LIVE LOAD 2 LIVE LOAD 0 0 -0.003 -0.003 0 0 0.003 0.003 0 0 0 0 0.001 0.001
Min rZ 1 1 2 LIVE LOAD 2 LIVE LOAD 0 0 -0.003 -0.003 0 0 0.003 0.003 0 0 0 0 -0.001 -0.001
Max Rst 7 7 2 LIVE LOAD 2 LIVE LOAD 0 0 -0.04 -0.035 0 0 0.04 0.035 0 0 0 0 0 0
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