V. AISC LRFD - Angle Section Tension Capacity

To check the adequacy of a L4X4X1/2 American single angle to carry a tensile design load of 120 Kips.

Reference

Hand calculation using the following reference:

AISC Load Factor Resistance Design, 3rd Edition, Example 3.2, case (a), page 3-7.

Problem

Assume the reduction in area due to bolt holes to be equivalent to a net section factor of 0.795.

F_y =36 ksi

Hand Calculation

Net section = 0.795(3.75 in.²) = 2.98 in.²

ϕ P_{n} = {\begin{matrix} ϕ_{t} F_{y} A_{g} = 0.9 (36 k s i) (3.75 {i n .}^{2}) = 121.5 k \\ ϕ_{t} F_{u} A_{e} = 0.75 (58 k s i) (2.98 {i n .}^{2}) = 129.6 k \end{matrix}

Comparison

The reported STAAD.Pro value is based on the term PNT in the STAAD.Pro output.

表 1. Comparison of results
Result Type		Theory	STAAD.Pro	Difference
Design strength (kips)		121.5	121.5	none

注記: The assumed NSF of 0.795 is comparable to the term Ae/Ag which evaluates to 2.98/3.75.

STAAD Input

The file C:\Users\Public\Public Documents\STAAD.Pro 2023\Samples \Verification Models\09 Steel Design\US\AISC\AISC LRFD - Angle Section Tension Capacity.STD is typically installed with the program.

STAAD SPACE TENSION CAPACITY PER AISC LRFD 3RD ED
START JOB INFORMATION
ENGINEER DATE 23-Sep-18
END JOB INFORMATION
*
*  OBJECTIVE : CHECKING THE DESIGN AXIAL TENSILE STRENGTH OF A
*  L4X4X1/2 AMERICAN SECTION. CAPACITY SHOULD BE 122 KIPS ACCORDING TO
*  EXAMPLE 3-2 ON PAGE 3-7 OF 3RD EDITION LRFD CODE.
*
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 0 10 0;
MEMBER INCIDENCES
1 1 2;
MEMBER PROPERTY AMERICAN
1 TABLE ST L40408
UNIT INCHES KIP
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 29000
POISSON 0.3
END DEFINE MATERIAL
UNIT FEET KIP
CONSTANTS
MATERIAL MATERIAL1 ALL
SUPPORTS
1 FIXED
LOAD 1
JOINT LOAD
2 FY 120
PERFORM ANALYSIS
UNIT INCHES KIP
PARAMETER 1
CODE LRFD
FU 58 ALL
* NSF = 2.98/3.75 = 0.795
NSF 0.795 ALL
TRACK 1 ALL
CHECK CODE ALL
FINISH

STAAD Output

                         STAAD.Pro CODE CHECKING - (LRFD 3RD EDITION)   v1.0
                         ***********************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
 MEMBER     TABLE       RESULT/   CRITICAL COND/     RATIO/     LOADING/
                          FX            MY             MZ       LOCATION
 =======================================================================
      1  ST   L40408                   (AISC SECTIONS)
                           PASS     LRFD-H1-1A-T       0.988         1
                      120.00 T          0.00           0.00        0.00
 +---------------------------------------------------------------------+
 | DESIGN STRENGTHS FOR MEMBER     1       UNITS - KIP IN              |
 | PNC=   34.36  PNT=  121.50  MNZ=   96.57  MNY=  134.69  VN=   25.92 | 
 +---------------------------------------------------------------------+