Simply Supported Beam Design with Torsional Loading - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Applications and Example Worksheets : Science and Engineering : applications/SimplySupportedBeam

Simply Supported Beam Design with Torsional Loading

Using AISC Steel Shapes v14.1 Data

Introduction

This application performs a design analysis on a simply supported beam with torsional loading for a W10X54 steel beam (as defined by the AISC Steel Shapes Database).

 

 

References:

• 

Simplified Design for Torsional Loading of Rolled Steel Members, Lin, P.H., Engineering Journal, AISC, 1977

• 

2010 Specification for Structural Steel Buildings (ANSI/AISC 360-10), Fourth Printing (https://www.aisc.org/content.aspx?id=2884)

 

You will need to install the AISC Shapes Database package from the MapleCloud before you can use this application.

 

Load the AISC Package

withAISCShapes:

withUnitsStandard:

 

Data from the AISC Shapes Database for Steel Shape W10X54

CwPropertyW10X54,Cw;PropertyW10X54,Cw,metadata

Cw2320.0in6

Warping constant

(3.1)

JTPropertyW10X54,J;PropertyW10X54,J,metadata

JT1.82in4

Torsional moment of inertia

(3.2)

dPropertyW10X54,d;PropertyW10X54,d,metadata

d10.1in

Overall depth of member, or width of shorter leg for angles, or width of the outstanding legs of long legs back-to-back double angles, or the width of the back-to-back legs of short legs back-to-back double angles

(3.3)

SxPropertyW10X54,Sx;PropertyW10X54,Sx,metadata

Sx60.0in3

Elastic section modulus about the x-axis

(3.4)

SyPropertyW10X54,Sy;PropertyW10X54,Sy,metadata

Sy20.6in3

Elastic section modulus about the y-axis

(3.5)

rxPropertyW10X54,rx;PropertyW10X54,rx,metadata

rx4.37in

Radius of gyration about the x-axis = sqrt(Ix/A)

(3.6)

APropertyW10X54,A;PropertyW10X54,A,metadata

A15.8in2

Cross-sectional area of member

(3.7)

ZxPropertyW10X54,Zx;PropertyW10X54,Zx,metadata

Zx66.6in3

Plastic section modulus about the x-axis

(3.8)

IxPropertyW10X54,Ix;PropertyW10X54,Ix,metadata

Ix303.0in4

Moment of inertia about the x-axis

(3.9)

IyPropertyW10X54,Iy;PropertyW10X54,Iy,metadata

Iy103.0in4

Moment of inertia about the y-axis

(3.10)

 

Parameters

Gravity distributed load:

w1.15kipfft:


Lateral point load at the middle:

F5kipf:


Torsion at mid-span:

T5.1ft kipf:


Axial Load:

P96kipf:


Beam length:

L15ft:


Beam yield stress:

Fy50ksi:


Vertical bending unbraced length:

Lb15ft:


Axial vertical unbraced length:

Lx15ft:


Axial horizontal unbraced length:

Ly7.5ft:


Young's modulus and shear modulus:

E29000ksi:

G11200ksi:


Torsional property (Phillip, 1977):

λGJTECw

0.017406109611in

(4.1)

Determine Governing Moments at Middle of Span

Flexural moment:

MxwL28

32.34footkipf

(5.1)

MyFL4.0

18.75footkipf

(5.2)

M0TL4d

22.72footkipf

(5.3)

Philip page 101

β4sinhλL22λLsinhλL

β0.5850278056

(5.4)

Torsional moment:

MTβM0

13.29footkipf

(5.5)

 

Check Torsional Capacity (AISC 360-10 H3.3 & Philip page 100)

Maximum combined normal stress at the load point:

fbxMxSx+2MTSy

21.96kipfinch2

(6.1)

Safety factor for compression:

Ω1.67:

FnxFyΩ

29.94ksi

(6.2)

fbxFnx

0.7333393767

(6.3)

This is less then 1, so it is satisfactory.

 

Check Combined Compression and Bending Capacity (AISC 360-10, H1)

MrxMxSx+2MTSySx

109.78footkipf

(7.1)

Effective length factor:

K0.85:


Elastic bucking stress:

Feπ2EKLrx2

233.50ksi

(7.2)

Critical stress:

Fcr0.658FyFeFy

45.71ksi

(7.3)

PnFcrA

722.27kipf

(7.4)

 Allowable axial strength:

PcPnΩ

432.50kipf

(7.5)

This is greater than 3/4 Pr, so it is satisfactory.

 

Available flexural strength (Chapter F AISC 360-10):

 

MnminFyZx,FySx

250.00footkipf

(7.6)

McxMnΩ

149.70footkipf

(7.7)

This is greater than Mrx, so it is satisfactory.

McyMnΩ

149.70footkipf

(7.8)

These should be below 1 for a satisfactory design.

PPc+89MrxMcx+MyMcy

.99

(7.9)

Determine Deflections

Max twist angle (Lin, p100 eq4) in degrees:

φT2GJTλλL22sinhλL2sinhλLsinhλL2

φ0.2304416908

(8.1)

I3Ixsin90φπ1802+Iycos90φπ1802

303.00in4

(8.2)

I4Ixcos90φπ1802+Iysin90φπ1802

103.00in4

(8.3)

Vertical deflection at the middle:

Δvert  5wL4384EI3

.15in

(8.4)

Horizontal deflection at the middle:

Δhoriz  FL348EI4

.20in

(8.5)