Prob. 4 (30 pts)

A simply supported beam with w10:12 steel wide-flange

shape is loaded as shown in Figure.

The reactions at A and B are also given in Figure.

(A) Using Singularity functions, find the moment equation

and determine the maximum normal stress at D.

(B) Find the deflection at D, (x=7 ft) if E=30x10³ ksi.

Wide-Flange Sections or W Shapes FPS Units

Designation

in. x b/ft

W12 x 87

W12 x 50

W12 x 45

W12 x 26

W12 x 22

W12 x 16

W12 x 14

6X OLA

W10 x 100

W10 54

15.8

W10 x 45 13.3 10,10

11.5

9.92

10,47

5.62 10.24

4.41

9.99

3.54

9.87

VID x 30

W10 x 19

15

x 12

W x 67

W8 x 58

W X4

W x 40

x 31

5x24

W6 x 25

W6 x 20

W6 x 16

9

Area Depth

A

d

in²

25.6

14.7

13.2

W6 x 9

12.53

12.19

12.06

7.65 12.22

6.48

12.31

4.71

11.99

4.16 11.91

8.84

19.7

17.1

14.1

11.7

9.13

11.10

10.09

7.08

4.44

9.00

8.75

8.50

8.25

8.00

7.93

K11

7.34 6.38

5.87 6.20

4.74

6.28

4.43

5.99

3.55

2.68 5.90

Web

thickness

L

0.515

0.370

0.315

0.230

0.260

0.220

0.200

0.370

0.350

0.315

0.300

0.250

0.230

0.190

0.570

0.510

0.680 10.340

10.030

0.400

0.360

0.285

0.245

0.245

Flange

0.320

0.260

0.360

0.230

0.230

0.170

width

b

T

inª

12.125

0.810

740

8.080

0.640

8.045

0.575

350

6.490 0,380 204

4.030

0.425 156

3.990

3.970

8.020

7.985

5.810

thickness

4

4.020

4.000

3,960

0.365

0.225

1.130

0.615

0.630

0.530

0.510

0.395

6.270

0.210

0.935

0.810

0.400

0.315

103

88.6

8.280

272

8.220

228

8.110 0.685

184

8.070 0.560 146

7.995

0.435

110

6.495

4.015

6,080

6.000

4.000 0.405

5.990

0.360

4.000

0.280

3940 0.215

0.455

0.365

X-Xaxi

S

in²

118

3 kips/ft

623 112

303

60.0

248

209

170

13 kip

3 ft

32.4

18.8

68.9 13.8

53.8

10.9

J

in

I

in

4.60

4.37 103

48.0

53.4

16.7 2.70

41.4 13.4 2.66

10.2 2.60

32.1

29.1

22.1

5.38 241

39.7 3.07

64.7

5.18

13.9

1.96

58.1 5.15

50.0 124

194

31.4 5.17 17.3 5.34

25.4 4.91 4.66 2.31

17.1 4.67 2.82 1.41

14.9

4.62

2.36 1.19

8 kips

y-y axis

S

53.4

F

in² in

207 40.0

20.6

2.65

2.56

2.01

4.27

1.98

4.38

1.37

4.14

4.29 2.14

0.874

1.95 2.89 1.45

0.810

3.90

2.18 1.10 0785

88.6 21.4 2.12

52.0 3.65 75.1 18.3 2.10

361 60.9 15.0 2.08

60.4 3.72

43.3

35.5 1.91 49.1 122 2.04

21.5 3.47 37.1 9:27

20.9 3.42

11.8

3.29

D

133

11.3

16.7 5.75

18.3

3.41 1.70

1.51

0.347

9.72 256

7.31 2.49

1.50

16.4 5.56 247 2.19 1.11

0.773

0.753

2.02

1.61

0.876

17.1 5.61 1.52

133 4.41 1.50

4.43 2.20 0.966

1.46

9.32 3.11

0.918

0.905

E

3 kips/ft

13 kip

3 ft