1 VukazichCE160TrussDeflectionsusingMethodofVirtualWork[13]

CE 160 Notes: Truss Deflections Using Method of Virtual Work

A truss made of steel members is pin supported at point a, roller supported at point b and subjected to a point loads at points c and e as shown. The cross sectional areas of each member are shown on the figure. Find the horizontal and vertical deflection of point e using the Method of Virtual Work.

Use E = 30,000 ksi.

e

20 ft

15 ft 15 ft

c d

a b

24 k

20 ft 3 in2 3 in2

3 in2

1 in2

3 in2

1 in2

1 in2

12 k

δH#

δV#

2 VukazichCE160TrussDeflectionsusingMethodofVirtualWork[13]

Real System

Find truss member forces using method of joints (or method of sections)

Note: Tensile forces are positive

Virtual System to measure horizontal displacement at point e - δH

e

20 ft

30 ft

cd

a b

24 k

20 ft (20 k) (-16 k)

(-16 k)

(0)

(-20 k)

(40 k)

(12 k)32 k

36 k

32 k

12 k

3 VukazichCE160TrussDeflectionsusingMethodofVirtualWork[13]

Find truss member forces using method of joints (or method of sections)

Note: Tensile forces are positive

20 ft

1

20 ft

e

15 ft 15 ft

cd

a b

1e

20 ft

30 ft

cd

a b

20 ft (1.667) (-1.333)

(-1.333)

(0)

(1.667)

(0)

1 k

1.333 1.333

(0)

4 VukazichCE160TrussDeflectionsusingMethodofVirtualWork[13]

Method of Virtual Work to find δH

1 ∙ 𝛿! = 𝐹!"𝐹!"𝐿!𝐴!𝐸!

!

!!!

1 ∙ 𝛿! = 𝐹!"#𝐹!"#𝐿!"𝐴!"𝐸

+ 𝐹!"#𝐹!"#𝐿!"𝐴!"𝐸

+ 𝐹!"#𝐹!"#𝐿!"𝐴!"𝐸

+ 𝐹!"#𝐹!"#𝐿!"𝐴!"𝐸

1 ∙ 𝛿! = 1.66740 𝑘 25 𝑓𝑡 12 𝑖𝑛/𝑓𝑡3 𝑖𝑛! 30,000 𝑘𝑠𝑖 + 1.667

20 𝑘 25 𝑓𝑡 12 𝑖𝑛/𝑓𝑡3 𝑖𝑛! 30,000 𝑘𝑠𝑖

+ −1.333−16 𝑘 20 𝑓𝑡 12 𝑖𝑛/𝑓𝑡

3 𝑖𝑛! 30,000 𝑘𝑠𝑖 + −1.333−16 𝑘 20 𝑓𝑡 12 𝑖𝑛/𝑓𝑡

3 𝑖𝑛! 30,000 𝑘𝑠𝑖

𝛿! = 0.2222 𝑖𝑛 + 0.1111 𝑖𝑛 + 0.05689 𝑖𝑛 + 0.0569 𝑖𝑛

𝜹𝑯 = 𝟎.𝟒𝟒𝟕 𝒊𝒏 (positive, so deflection is in same direction as virtual load - to the right)

Virtual System to measure vertical displacement at point e – δV

Find truss member forces using method of joints (or method of sections)

20 ft

1

20 ft

e

15 ft 15 ft

cd

a b

5 VukazichCE160TrussDeflectionsusingMethodofVirtualWork[13]

Note: Tensile forces are positive

Method of Virtual Work to find δV

1 ∙ 𝛿! = 𝐹!"𝐹!"𝐿!𝐴!𝐸!

!

!!!

1 ∙ 𝛿! = 𝐹!"#𝐹!"#𝐿!"𝐴!"𝐸

+ 𝐹!"#𝐹!"#𝐿!"𝐴!"𝐸

1 ∙ 𝛿! = −1.0−16 𝑘 20 𝑓𝑡 12 𝑖𝑛/𝑓𝑡

3 𝑖𝑛! 30,000 𝑘𝑠𝑖 + −1.0−16 𝑘 20 𝑓𝑡 12 𝑖𝑛/𝑓𝑡

3 𝑖𝑛! 30,000 𝑘𝑠𝑖

𝛿! = 0.04267 𝑖𝑛 + 0.04267 𝑖𝑛

𝜹𝑽 = 𝟎.𝟎𝟖𝟓𝟑 𝒊𝒏 (positive, so deflection is in same direction as virtual load - down)

1

e

20 ft

30 ft

cd

a b

20 ft (0) (-1.0)

(-1.0)

(0)

(0)

(0)1.0

(0)