1. Shear and Moment Equations
1 kip/ft
20 feet
10 kip
V (kip) 10
-10 x
V(x) = ?
Symmetric beam – what are the reactions?
How would you find an equation for shear, V(x)?

2. Shear and Moment Equations
1 kip/ft
20 feet
10 kip
V (kip) 10
-10 x
V(x) = mx + b

3. Shear and Moment Equations
1 kip/ft
20 feet
10 kip
V (kip) 10
-10 x
V(x) = -1kip/ft x + 10 kip
Is it a coincidence that w and the slope have the same magnitude? (NO!)

4. 1 kip/ft 20 feet 10 kip 10 V(x) = -1kip/ft x + 10 kip V (kip) x -10 50
How would you find an equation for Moment, M(x)?
M (kip-ft)
M(x) = ? x

5. 1 kip/ft 20 feet 10 kip 10 V(x) = -1kip/ft x + 10 kip V (kip) x -10 50
How would you find an equation for Moment, M(x)?
M (kip-ft)
M(x) = ∫ V(x) x

6. 1 kip/ft 20 feet 10 kip 10 V(x) = -1kip/ft x + 10 kip V (kip) x -10 50
How would you find an equation for Moment, M(x)?
M (kip-ft)
M(x) = ∫-1kip/ft x + 10 kip x

7. 1 kip/ft 20 feet 10 kip 10 V(x) = -1kip/ft x + 10 kip V (kip) x -10 50
M(0) = 0
How would you find an equation for Moment, M(x)?
M (kip-ft) 2 1 ft
kip
M(x)= x + 10 kip x + C 2 x

8. 1 kip/ft 20 feet 10 kip 10 V(x) = -1kip/ft x + 10 kip V (kip) x -10 50
M(0) = 0
M (kip-ft) 2 1 ft
kip
M(x)= x + 10 kip x 2 x