Lumped Mass Method Example

Method 1: SEISMIC ANALYSIS USING LUMPED MASS METHOD Data: Building size : Length= 15m (5 Bays each 3.0m) Width = 15m (5 Bays each 3.0m) Height =33m (11 Bays each 3.0m) Concrete Mix M30 Steel Fe415 Loads: LL =1.50 KN/m2 (For Roof slab) 2.0KN/m2 (For floor slab) Member sizes : Beam 300 x 450mm; Column 450 x 300 mm Slab thickness: 120mm.

15.00

Soil type: medium. Zone :III Importance factor=1.50

BEAMS ARE OF SIZE 0.3 X 0.45

3.00

3.00

3.00

3.00

3.00

15.00

COLUMN ARE OF SIZE 0.45 X 0.30

PLAN

33.00 3.00

BEAMS SIZE 0.3 X 0.45

COLUMN SIZE 0.45 X 0.30 3.00

3.00

3.00

3.00

3.00

15.00

ELEVATION

1. Geometry Creation : New Project  Select  Space  Length =meters; Force=KN; File Name=Seismic Coefficient method (LM)  Next Select  Open Structure Wizard  Finish. Change to Frame models from Truss models  Select Bay Frame and double click on it. Length X=15.0m No. of Bays =5 Height Y=3.0m Width Z=15.0m

No. of Bay=1

Each Bay =3.0m Each Bay =3.0m

No. of Bays=5

Apply Transfer Model YesOk.

Each Bay =3.0m

Go to front view. 2.Member Property: Click General  Property Define  Rectangle

YD=0.45

ZD=0.30 

Add  YD=0.45 ZD=0.30  AddClose . Highlight 0.45 x 0.30 Main menu Select Beam parallel to  X , Select  Beam parallel to  Z   Assign to selected beam  Assign Yes  Highlight 0.45 x 0.30 Select Beam parallel to Y   Assign to selected beam  Assign Yes Close. Select Beam cursor and select entire structureClick Translational Repeat icon Y

No. of steps=10 Default spacing=3m  link  OK.

3. Supports : Go to front view. Click Support  Create  Fixed Add. Highlight support 2 and select bottom support nodes by windowing using node cursor  Assign to selected nodes  Assign Yes  Close  De select the nodes and change to beam cursor. 4. Loads -Seismic Definition : Main menu Commands  Loading  Definitions Seismic load IS 18932002. Seismic Parameters appear. Select IS1893-2002. Click Generate  Add. IS1893 seismic parameters screen will appear. Select Zone =III. Response Reduction Factor: Specicial RC MRF=5 Importance factor (I) =1.5 Rock/soil type (SS) :2 (For Medium soil). Structure Type: (Optional) =1 (For RC Frame Building). Damping Ratio (DM)= 0.05% Period in X direction= 0.09 h =0.09 x33 √dx

√12

=0.86 sec.

Period in Z direction= 0.09 h =0.09 x33 √dZ

=0.86 sec.

√12

Generate  Add  Close. Click Zone 0.16 RF 5 I 1.5 SS 2 ST 1 DM 0.05 0.86 0.86  Add  Click Joint Weights Add  Close. ************************* To Find Joint Weight 1. Geometry Creation : New Project 

Select  Space  Length =meters; Force=KN;

File Name=Joint weight  Next Select  Open Structure Wizard  Finish. Change to Frame models from Truss models  Select Bay Frame and double click On it. Length X=15.0m No. of Bays =5 Height Y=33.0m Width Z=15.0m

Each Bay =3.0m

No. of Bays=11 Each Bay =3.0m No. of Bays=5

Each Bay =3.0m

Apply Transfer Model YesOk. Go to front view. 2. Member Property : Click General  Property Define  Rectangle

YD=0.45

ZD=0.30 

Add  YD=0.45 ZD=0.30  AddClose . Highlight 0.45 x 0.30 Main menu Select Beam parallel to  X , Select  Beam parallel to  Z   Assign to selected beam  Assign Yes  Highlight 0.45 x 0.30 Select Beam parallel to Y   Assign to selected beam  Assign Yes Close. 3. Loads: Click Load and Definition  Load case details  Add.

Number 1.

Loading Type: Dead.

Title: DL  Add. Number 2. Loading Type: Live. Title: LL  Add. Click load case details Add. Click Load comb Title: Load comb No.3 Name: 1.5 (DL+LL) Add. Click Load case 1  Add.  Self weight  Selfweight Y Factor =-1  GY Add. Click Member Load Uniform force  Y direction w1=-12KN/m  Add. w1=-6KN/m Add. . w1=-4KN/m Add. Click Floor Load  Pressure =-4KN/m2 Y range Mini =3.0m Max =30.0m  Add. Pressure =-5.25Kn/m2 Y range Mini=30.2 Max=33.0  Add. Click Load case 2 detailsAdd. Floor Load  Pressure=-2KN/m2 Y range Mini=3.0

Max=30.0  Add.

Pressure=-1.50KN/m2 Y range Mini=30.2

Max=33.0 Add.

Highlight SelfweightAssign to view Assign. Highlight Member load - 12 KN/m  Go to Front view  Select Beam parallel toX and Z. Front elevation view. Right click   New view  Ok. Select only typical floor beams except roof beam   create new view Ok. Plan view  Highlight w1=-12Select the outer portion of beams (9” wall portion )   Assign to selected beams Assign Yes. Highlight -6 KN/mFront view  Select inner portion of beam  Assign to selected beam Assign  Yes. Go to front view  select top portion by windowing Right clickNew view OK. Plan viewselect only outer portion and click -4 KN/m  Assign to selected

beamAssign  Yes. 2.Support: Support Create  Pinned  Add. Click Support 2  Assign to view Assign  Close. 3.Analysis/Print Perform Analysis  No print  Add. 4.Post Print Define Commands Support Reaction  Add. 5.Define Commands  Load List Select Load Comb 3 from list Add. 6.Analysis  Run Analysis Done. 7.Go to Post Processing Click Report set up. Select Load case 3OK. Click Items  Select output from list  select Reactions and sent to right in selected list  OK. Go to File  Export report  MS word file. From the File copy support reaction and paste it in a separate excel file. Select Node No., Fy from the file and copy & paste it in a separate place. In between Node No. and Fy, type “ weight” and copy for all nodes. Copy Node No. Weight Fy values from Excell file and paste it below . Joint Weight of first file example in lumped mass. Now add the following loads: Seismic Loads: Click Load case details  Add. Number 1 Loading Type : Seismic Title: EQ X+ve  Add. Number 2 Loading Type : Seismic Title: EQ X -ve  Add. Number 3. Loading Type : Seismic Title: EQ Z+ve  Add. Number 4. Loading Type : Seismic Title: EQ Z -ve  Add. Highlight EQ X +ve  Add. Seismic load  X Direction Factor=1  Add.

Highlight EQ X -ve  Add. Seismic load  X Direction Factor= -1  Add. Highlight EQ Z +ve  Add. Seismic load  Z Direction Factor=1  Add. Highlight EQ Z -ve  Add. Seismic load  Z Direction Factor= -1  Add. Dead Load: Click load case details  Add. Number 5. Loading Type: dead. Title: DL  Add. Live load: Click load case details  Add. Number 6. Loading Type: Live. Title: LL  Add. Click DL Add. Self weight Self weight  Y Factor =-1.  Add. Member load Uniform Force W1=-12 KN/m  GY Add. w1=-6KN/m Add. w1=4KN/m  Add. Floor Load Pressure =-4KN/m2 Y range Mini=3.0m Max=30.0m  Add. Pressure =-5.25 KN/m2 Y range Mini=30.2 Max = 33.0  Add. Click LL  Add. Floor load  Pressure=-2 KN/m2 Y range Mini=3.0 Max = 30.0m  Add. Pressure=-1.50 KN/m2 Y range Mini=30.2 Max = 33.0m  Add. Highlight Selfweight  Assign to view  Assign. Highlight Member load - 12 KN/m  Go to Front view  Select Beam parallel toX and Z. Front elevation view. Right click   New view  Ok.

Select only typical floor beams except roof beam   create new view Ok. Plan view  Highlight w1=-12Select the outer portion of beams (9” wall portion )   Assign to selected beams Assign yes. Highlight - 6 KN/m  Select interior wall   Assign to selected beam  AssignYes. Go to Front view  Highlight - 4 KN/mselect top portion by windowing  Right click   New view  create a New view  OK. Plan view  Select outer portion of the beam   Assign to selected beam  AssignYes. To give Perform analysis - change command: High Light Load case 2: EQ in X-Ve. Click Analysis/Print Perform Analysis Load Data Add  Check □ After current Click Change Add  Check □ After current. High Light Load case 3: EQ in Z+Ve. Click Analysis/Print Perform Analysis Load Data Add  Check □ After current Click Change Add  Check □ After current. High Light Load case 4: EQ in Z-Ve. Click Analysis/Print Perform Analysis Load Data Add  Check □ After current Click Change Add  Check □ After current. Load combinations: Commands  Loading  Edit Auto loads Select Indian code Select: New category Category name: say EQ No. of Rule:4 Rule No.

Dead

Live

seismic

1 1.5 2 1.5 3 1.2 4 0.9 Click update Table Close.

1.5 --1.2 ---

-1.5 1.2 1.5

Click Load case details  Auto Load comb select Indian Code category : EQ Generate Loads  Add  Close. Main menu Commands  Loading Load List (Select Load comb 7 to 19 )  Load list OKClose. Design: Click DesignConcrete Current code IS 456Define Parameters Fc=30,000KN/m2 Add. Fymain=415,000KN/m2 Add. Fysec=415,000KN/m2 Add. Ratio=3%Add. Click CommandDesign beam Add. Design column Add. Take offAddClose. Click Fck=30,000KN/m2 and select the entire structure  Assign to selected beam Assign Yes. Click Fymain=415000KN/m2 and select the entire structure  Assign to selected beam Assign Yes. Click Fysec=415000KN/m2 and select the entire structure  Assign to selected beam Assign Yes. Click Ratio=3% and select the entire structure  Assign to selected beam Assign Yes. Click design beam SelectBeam parallel to X and beam parallel to Z Assign to selected beam Assign Yes . Click Design ColumnSelect  Beam parallel to Y Assign to selected beam Assign Yes.

Note: Save the File and Run the Program. Analysis type: Main menu  CommandsAnalysisPerform Analysis No print  OK. Post Analysis Print: Main menuCommandsPost analysis print Support Reactions  To view  OK. Analysis: Main menuAnalysisRun AnalysisDone. Result: Click Post processing. view deflection for various loads. Bending moment Mz: Click Mz icon. Results View value Beam results Bending □ Ends □ Mid span Annotate Close. Shear force Fy: Click Fy icon. Results View value Beam results Shear □ Ends  Annotate Close. (Before click shear force remove previous selection mark) Axial Force Fx: Click Fx icon. Results View value Beam results Axial r □ Ends  Annotate Close. Design Check: Main menu SelectBy specification All failed beams. Go to modeling mode. Select column ( at bottom portion) Double click the columnConcrete design. Check the bottom most storey column. If some columns in GF inner are failed, change the size of

the column for inner portion and again run the analysis, verify the result. Similarly check the beam by double click the particular beam for find the reinforcement. If all are passed ok. Otherwise revise the beam section if failed. Report: Click Report setup icon Click input from available from left side. Select sections , Loadings and sent to Right side by clicking > Select output. From output select Beam end forces, reactions, shear forces, axial forces, Beam force detail summary. To Take picture: Click take picture icon Enter the title of the sketch. Then Go to report set up. Select picture Album. If you want to change the sketch title enter the title in caption. Adjust the picture size by adjusting height & width. Select □ Full page. To export Results in word file: File  Export Report  MS word file. Click save. Note: This procedure is very useful in the older version of Staad Pro due to the fact that in the OLDER version, load list in load cases differ from the load list in load definition.

In the latter version of Staad Pro 2007, you can just copy paste the loads from the load cases to the seismic definition and let Staad will do the entire process of analysing weights but of course there is a need to carefully change some load name, e.g. instead of floor load that will be floor weights Member Load will be Member weight etc. It's much easier. This method of analyzing Earthquake analysis by direct method as MEMBER WEIGHT METHOD is explained separately.