V. 3x2 Plane Frame Moments

To find the bending moments due to lateral joint loads in a 3x2 bay plane frame.

Reference

Noris and Wilbur, Elementary Structural Analysis, 2nd Edition, McGraw – Hill, Inc., Page 304.

Problem

Determine the bending moments in the members of frame.

E = 30,000 ksi

I_AE = I_EI = 240 in⁴

I_BF = I_FJ = 480 in⁴

I_CG = I_GK = 600 in⁴

I_DH = I_HL = 360 in⁴

I_EF = I_IJ = 600 in⁴

I_FG = I_JK = 1,200 in⁴

I_GH = I_KL = 1,800 in⁴

3x2 bay plane frame

Comparison

Table 1. Comparison of results
Result Type		Theory	STAAD.Pro	Difference
Bending in member (ft·kips)	AE	29.6	29.80	<1%
	EA	25.1	25.21	none
	EI	6.5	6.44	<1%
	IE	10.6	10.48	1.1%
	BF	60.9	61.03	none
	FB	53.7	53.69	none
	FJ	18.3	18.50	1.1%
	JF	24.8	24.84	none
	CG	76.8	76.70	none
	GC	68.3	68.24	none
	GK	25.2	25.25	none
	KG	32.4	32.52	none
	DH	45.6	45.45	none
	HD	40.1	39.87	<1%
	HL	13.5	13.58	<1%
	LH	18.5	18.39	<1%
	EF	31.6	-31.65	none
	FE	29.5	-29.35	<1%
	IJ	10.6	-10.48	1.1%
	JI	10.0	-9.79	2.1%
	FG	42.5	-42.84	<1%
	GF	41.3	-41.71	<1%
	JK	14.8	-15.05	1.7%
	KJ	14.4	-14.71	2.2%
	GH	52.2	-51.78	<1%
	HG	53.6	-53.45	none
	KL	18.0	-17.81	1.1%
	LK	18.5	-18.39	<1%

STAAD Input

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\03 Frames\3x2 Plane Frame Moments.STD is typically installed with the program.

STAAD PLANE :A 3X2 BAY PLANE FRAME
START JOB INFORMATION
ENGINEER DATE 17-Sep-18
END JOB INFORMATION
*
* REFERENCE: ELEMENTARY STRUCTURAL ANALYSIS, NORIS AND WILBUR, 2ND
*   EDITION. MCGRAW-HILL BOOK COMPANY, PAGE 304, WORKOUT PROBLEM
*
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 0 20 0; 3 0 35 0; 4 20 0 0; 5 20 20 0; 6 20 35 0; 7 45 0 0;
8 45 20 0; 9 45 35 0; 10 75 0 0; 11 75 20 0; 12 75 35 0;
MEMBER INCIDENCES
1 1 2; 2 2 3; 3 4 5; 4 5 6; 5 7 8; 6 8 9; 7 10 11; 8 11 12; 9 2 5;
10 5 8; 11 8 11; 12 3 6; 13 6 9; 14 9 12;
UNIT INCHES KIP
MEMBER PROPERTY AMERICAN
1 2 PRIS AX 10 IZ 240
3 4 PRIS AX 15 IZ 480
5 6 PRIS AX 20 IZ 600
7 8 PRIS AX 12 IZ 360
9 12 PRIS AX 20 IZ 600
10 13 PRIS AX 30 IZ 1200
11 14 PRIS AX 35 IZ 1800
UNIT FEET KIP
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 4.32e+06
POISSON 0.290909
END DEFINE MATERIAL
UNIT INCHES KIP
CONSTANTS
MATERIAL MATERIAL1 ALL
SUPPORTS
1 4 7 10 FIXED
LOAD 1 HORIZONTAL JOINT LOAD
JOINT LOAD
2 3 FX 10
UNIT FEET KIP
PERFORM ANALYSIS
PRINT MEMBER FORCES ALL
FINISH

STAAD Output

   MEMBER END FORCES    STRUCTURE TYPE = PLANE
   -----------------
   ALL UNITS ARE -- KIP  FEET     (LOCAL )
  MEMBER  LOAD  JT     AXIAL   SHEAR-Y  SHEAR-Z   TORSION     MOM-Y      MOM-Z
      1    1     1     -4.06      2.75     0.00      0.00      0.00      29.80
                 2      4.06     -2.75     0.00      0.00      0.00      25.21
      2    1     2     -1.01      1.13     0.00      0.00      0.00       6.44
                 3      1.01     -1.13     0.00      0.00      0.00      10.48
      3    1     4     -0.51      5.74     0.00      0.00      0.00      61.03
                 5      0.51     -5.74     0.00      0.00      0.00      53.69
      4    1     5     -0.18      2.89     0.00      0.00      0.00      18.50
                 6      0.18     -2.89     0.00      0.00      0.00      24.84
      5    1     7     -0.14      7.25     0.00      0.00      0.00      76.70
                 8      0.14     -7.25     0.00      0.00      0.00      68.24
      6    1     8     -0.02      3.85     0.00      0.00      0.00      25.25
                 9      0.02     -3.85     0.00      0.00      0.00      32.52
      7    1    10      4.71      4.27     0.00      0.00      0.00      45.45
                11     -4.71     -4.27     0.00      0.00      0.00      39.87
      8    1    11      1.21      2.13     0.00      0.00      0.00      13.58
                12     -1.21     -2.13     0.00      0.00      0.00      18.39
      9    1     2      8.38     -3.05     0.00      0.00      0.00     -31.65
                 5     -8.38      3.05     0.00      0.00      0.00     -29.35
     10    1     5      5.53     -3.38     0.00      0.00      0.00     -42.84
                 8     -5.53      3.38     0.00      0.00      0.00     -41.71
     11    1     8      2.14     -3.51     0.00      0.00      0.00     -51.78
                11     -2.14      3.51     0.00      0.00      0.00     -53.45
     12    1     3      8.87     -1.01     0.00      0.00      0.00     -10.48
                 6     -8.87      1.01     0.00      0.00      0.00      -9.79
     13    1     6      5.98     -1.19     0.00      0.00      0.00     -15.05
                 9     -5.98      1.19     0.00      0.00      0.00     -14.71
     14    1     9      2.13     -1.21     0.00      0.00      0.00     -17.81
                12     -2.13      1.21     0.00      0.00      0.00     -18.39
      :A 3X2 BAY PLANE FRAME                                   -- PAGE NO.    4