Combined Stress. Homework 11 Lab 08

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Combined

Stress

Homework 11

Lab 08

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Combined

Stress

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Combined

Stress

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Combined

Stress

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Combined

Stress

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Combined

Stress

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Combined

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Combined

Stress

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The given roof truss carries both an exterior snow load and an interior (attic) floor load. Determine the member forces and stresses and calculate the combined stress levels (top and bottom) for the lower chord member using the NDS combined stress equations. Consider all joints pinned, with simple (joint to joint) members. The given allowable stresses (F't and F'b) are for southern pine with all adjustment factors already applied.

Datasheet

Full span of truss Height of truss

On Center spacing of trusses Size of bottom chord Actual width, b Actual depth, d Snow Load on roof, w1 Live Load in attic, w2 Fac. allow. bending stress, F’b Fac. allow. tension stress, F't

21FT 5FT 16IN 4x5 3.5IN 4.5IN 35PSF 100PSF 1150PSI 690PSI Questions

1. Load on one truss - top chord, w1 2. Load on one truss - bottom chord, w2 3. Total left reaction due to w1 and w2

4. Vertical force component in truss top chord (no sign) 5. Horizontal force component in truss top chord (no sign) 6. Axial force in the truss bottom chord. (- if compression) 7. Area of the bottom chord member

8. Axial stress in the bottom chord. (- if compression) 9. Maximum bending moment in the bottom chord member 10. Section modulus of the bottom chord member, Sx 11. Maximum bending stress in the bottom chord member 12. Combined stress using NSD equation 3.9-1 13. Combined stress using NSD equation 3.9-2 14. Does member pass? 1=passes 0=fails

Combined

Stress

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Main Steps

1. Determine truss joint loading

2. Determine the external end reactions

of the whole truss.

3. Use an FBD of the reaction joint to find

the chord forces.

4. Calculate the actual axial and flexural

stress.

5. Check NDS Equations

(Factored Allowable Stress Known)

Datasheet

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1. Determine truss joint loading

1. Load on one truss - top chord, w1

W1,PLF = W1,PSFx O.C = 35 x 16/12 = 46.67 PLF

2. Load on one truss - bottom chord, w2

W2,PLF = W2,PSFx O.C = 100 x 16/12 = 133.33 PLF

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Pointed Load W1= W1,PLFx S = 46.67 x 21 = 980.07 LBS

Pointed Load W2= W2,PLFx S = 133.33 x 21 = 2799.93 LBS

Datasheet

21FT 5FT 16IN 4x5 3.5IN 4.5IN 35PSF 100PSF 1150PSI 690PSI Related Questions

1. Load on one truss - top chord, w1 2. Load on one truss - bottom chord, w2

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2. Determine the external end

reactions of the whole truss.

3. Total left reaction due to w1 and w2

RA= RB= (W1+ W2)/2 = (980.07 + 2799.93)/2 = 1890 LBS

Datasheet

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3. Use an FBD of the reaction joint to

find the chord forces.

4. Vertical force component in truss top chord (no sign) ΣV = RA– W1/4 – W2/4 – VTop= 0

VTop= RA– W1/4 – W2/4 = 1890 – 980.07/4 – 2799.93/4 = 945 LBS

5. Horizontal force component in truss top chord (no sign) HTop= VTopx 10.5 / 5= 945 x 10.5 / 5 = 1984.5 LBS

6. Axial force in the truss bottom chord. (- if compression) ΣH = - HTop+ HBottom = 0

H_Bottom= H_Top= 1984.5 LBS (Tension)

Datasheet

4. Vertical force component in truss top chord (no sign) 5. Horizontal force component in truss top chord (no sign) 6. Axial force in the truss bottom chord. (- if compression)

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4. Calculate the actual axial and

flexural stress.

7. Area of the bottom chord member A = b x d = 3.5 x 4.5 = 15.75 IN2

8. Axial stress in the bottom chord. (- if compression) ft= HBottom/ A= 1984.5 / 15.75 = 126 PSI (Tension)

9. Maximum bending moment in the bottom chord member M = 1

8w2,PLF(𝑆𝑆2)2= 1

8x 133.33 x 10.52= 1837.45 PSI

10. Section modulus of the bottom chord member, Sx Sx= 11.81 IN3

11. Maximum bending stress in the bottom chord member fb= M/Sx= 1837.45 x 12 / 11.81 = 1867.01 PSI

Datasheet

7. Area of the bottom chord member

8. Axial stress in the bottom chord. (- if compression) 9. Maximum bending moment in the bottom chord

member

10. Section modulus of the bottom chord member, Sx 11. Maximum bending stress in the bottom chord member

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5. Check NDS Equations

(Factored Allowable Stress Known)

Datasheet

12. Combined stress using NSD equation 3.9-1 13. Combined stress using NSD equation 3.9-2 14. Does member pass? 1=passes 0=fails

12. Combined stress using NSD equation 3.9-1

𝑓𝑓𝑡𝑡 𝐹𝐹𝑡𝑡′+ 𝑓𝑓𝑏𝑏 𝐹𝐹𝑏𝑏∗= 126 690+ 1867.01 1150 = 1.806 > 1

13. Combined stress using NSD equation 3.9-2

𝑓𝑓𝑏𝑏− 𝑓𝑓𝑡𝑡 𝐹𝐹𝑏𝑏∗∗ =

(1867.01 −126)

1150 = 1.514 > 1

14. Does member pass? 1=passes 0=fails 0 = Fail

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Main Steps

1. Determine truss joint loading

2. Determine the external end reactions

of the whole truss.

3. Use an FBD of the reaction joint to find

the chord forces.

4. Calculate the actual axial and flexural

stress.

5. Determine allowable stresses using

applicable factors

Datasheet

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https://miro.com/a

pp/board/o9J_lLmd

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Lab 08

Combined

Stress

𝑀𝑀 =𝑃𝑃𝑃𝑃₄= 0.15 𝑥𝑥 12₄ = 0.45 IN-LBS 𝑓𝑓𝑏𝑏=_𝑆𝑆𝑀𝑀_𝑦𝑦=_0.00032550.45 = 1382 PSI 𝑓𝑓𝑡𝑡= 𝑓𝑓𝑐𝑐=𝑃𝑃_𝐴𝐴=_0.0312510 = 320 PSI

1. Flexure + Axial Tension

𝑓𝑓𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢= 𝑓𝑓𝑏𝑏− 𝑓𝑓𝑡𝑡= 1382 − 320 = 1062 PSI (Compression)

𝑓𝑓𝑙𝑙𝑙𝑙𝑙𝑙𝑢𝑢𝑢𝑢= 𝑓𝑓𝑏𝑏+ 𝑓𝑓𝑡𝑡= 1382 + 320 = 1702 PSI (Tension)

2. Flexure + Axial Compression

𝑓𝑓𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢= 𝑓𝑓𝑏𝑏+ 𝑓𝑓𝑐𝑐= 1382 + 320 = 1702 PSI (Compression)

𝑓𝑓𝑙𝑙𝑙𝑙𝑙𝑙𝑢𝑢𝑢𝑢= 𝑓𝑓𝑏𝑏− 𝑓𝑓𝑐𝑐= 1382 − 320 = 1062 PSI (Tension)

3. What additional load and stress is being neglected in the case of compression + flexure?

(starting from 12:40 of the video) 𝑓𝑓𝑐𝑐𝑙𝑙𝑐𝑐𝑏𝑏=_𝑆𝑆𝑀𝑀_𝑦𝑦±𝑃𝑃_𝐴𝐴±𝑃𝑃∆_𝑆𝑆_𝑦𝑦