Beams with partial distributed load

Roark's Formulas for Stress and Strain
Shear, moment, slope, deflection of elastic straight beams-table 8.1
W=load (N), w=unit load (N/mm), M0=applied couple (Nmm), θ0=angular displacement (degrees),
RA and RB are the vertical end reactions at left and right respectively (N),
MA and MB are the reaction end moments at left and right respectively (Nmm)

2. Partial distributed load

Unit load wa (N/mm):
Unit load wl (N/mm):
Distance l (mm):
Distance a (mm):
Elastic modulus E (MPa):
Moment of Inertia I (Nmm4):
Distance neutral axis to outer fiber v (mm):

2a. Left end free, right end fixed (cantilever)

RA (N):	RA	RB (N):	RB
MA (Nmm):	MA	MB (Nmm):	MB
σA (MPa):	σA	σB (MPa):	σB
θA (degrees):	θA	θB (degrees):	θB
deflection yA (mm):	yA	deflection yB (mm):	yB

If a=0 and wl = wa (uniform load on the entire span)

Max M = MB (Nmm):	maxM
Max σ = σB (MPa):	maxσ
Max θ = θA (degrees):	Maxθ
Max y = yA (mm):	maxY

If a=0 and wa = 0 (uniformly increasing load)

Max M = MB (Nmm):	maxM
Max σ = σB (MPa):	maxσ
Max θ = θA (degrees):	Maxθ
Max y = yA (mm):	maxY

If a=0 and wl = 0 (uniformly decreasing load)

Max M = MB (Nmm):	maxM
Max σ = σB (MPa):	maxsigma
Max θ = θA (degrees):	Maxθ
Max y = yA (mm)	maxY

2b. Left end guided, right end fixed

RA (N):	RA	RB (N):	RB
MA (Nmm):	MA	MB (Nmm):	MB
σA (MPa):	σA	σB (MPa):	σB
θA (degrees):	θA	θB (degrees):	θB
deflection yA (mm):	yA	deflection yB (mm):	yB

If a=0 and wl = wa (uniform load on the entire span)

Max -M = MB (Nmm):	max-M
Max -σ = σB (MPa):	max-σ
Max +M = MA (Nmm):	max+M
Max +σ = σA (MPa):	max+σ
Max y = yA (mm):	maxY

If a=0 and wa = 0 (uniformly increasing load)

Max -M = MB (Nmm):	max-M
Max -σ = σB (MPa):	max-σ
Max +M = MA (Nmm):	max+M
Max +σ = σA (MPa):	max+σ
Max y = yA (mm):	maxY

If a=0 and wl = 0 (uniformly decreasing load)

Max -M = MB (Nmm):	max-M
Max -σ = σB (MPa):	max-σ
Max +M = MA (Nmm):	max+M
Max +σ = σA (MPa):	max+σ
Max y = yA (mm):	maxY

2c. Left end simply supported, right end fixed

RA (N):	RA	RB (N):	RB
MA (Nmm):	MA	MB (Nmm):	MB
σA (MPa):	σA	σB (MPa):	σB
θA (degrees):	θA	θB (degrees):	θB
deflection yA (mm):	yA	deflection yB (mm):	yB

If a=0 and wl = wa (uniform load on the entire span)

RA (N):	RA	RB (N):	RB
Max +M (Nmm):	max+M	at x (mm) =	x
Max -M = MB (Nmm):	max-M	Max -σ = σB (MPa):	max-σ
Max +σ (MPa):	max+σ	Max θ = θA (degrees):	maxθ
Max y (mm)	maxY	at x (mm) =	x

If a=0 and wa = 0 (uniformly increasing load)

RA (N):	RA	RB (N):	RB
Max +M (Nmm):	max+M	at x (mm) =	x
Max -M = MB (Nmm):	max-M	Max -σ = σB (MPa):	max-σ
Max +σ (MPa):	max+σ	Max θ = θA (degrees):	maxθ
Max y (mm)	maxY	at x (mm) =	x

If a=0 and wl = 0 (uniformly decreasing load)

RA (N):	RA	RB (N):	RB
Max +M (Nmm):	max+M	at x (mm) =	x
Max -M = MB (Nmm):	max-M	Max -σ = σB (MPa):	max-σ
Max +σ (MPa):	max+σ	Max θ = θA (degrees):	maxθ
Max y (mm)	maxY	at x (mm) =	x

2d. Left end fixed, right end fixed

RA (N):	RA	RB (N):	RB
MA (Nmm):	MA	MB (Nmm):	MB
σA (MPa):	σA	σB (MPa):	σB
θA (degrees):	θA	θB (degrees):	θB
deflection yA (mm):	yA	deflection yB (mm):	yB

If a=0 and wl = wa (uniform load on the entire span)

Max +M (Nmm):	max+M	at x (mm) =	x
Max -M = MA=MB (Nmm):	max-M	Max -σ = σA= σB (MPa):	max-σ
Max +σ (MPa):	max+σ
Max y (mm)	maxY	at x (mm) =	x

If a=0 and wa = 0 (uniformly increasing load)

RA (N):	RA	RB (N):	RB
MA (Nmm):	MA	σA (MPa):	σA
Max +M (Nmm):	max+M	at x (mm) =	x
Max -M = MB (Nmm):	max-M	Max -σ = σB (MPa):	max-σ
Max +σ (MPa):	max+σ
Max y (mm)	maxY	at x (mm) =	x

2e. Left end simply supported, right end simply supported

RA (N):	RA	RB (N):	RB
MA (Nmm):	MA	MB (Nmm):	MB
σA (MPa):	sigmaA	σB (MPa):	σB
θA (degrees):	θA	θB (degrees):	θB
deflection yA (mm):	yA	deflection yB (mm):	yB

If a=0 and wl = wa (uniform load on the entire span)

RA (N):	RA	RB (N):	RB
Max M (Nmm):	maxM	when x (mm) =	x
Max σ (MPa):	maxσ	Max θ = θB (degrees)	maxθ
Max y (mm):	maxY	when x (mm)=	x

If a=0 and wa = 0 (uniformly increasing load)

RA (N):	RA	RB (N):	RB
Max M (Nmm):	maxM	when x (mm) =	x
Max σ (MPa):	maxσ
Max θ = θA (degrees)	maxθ	Max θ = θB (degrees)	maxθ
Max y (mm):	maxY	when x (mm)=	x

2f. Left end guided, right end simply supported

RA (N):	RA	RB (N):	RB
MA (Nmm):	MA	MB (Nmm):	MB
σA (MPa):	σA	σB (MPa):	σB
θA (degrees):	θA	θB (degrees):	θB
deflection yA (mm):	yA	deflection yB (mm):	yB

If a=0 and wl = wa (uniform load on the entire span)

Max M = MA(Nmm):	maxM
Max σ = σA(MPa):	maxσ
Max θ = θB (degrees)	maxθ
Max y = yA(mm):	maxY

If a=0 and wa = 0 (uniformly increasing load)

Max M = MA(Nmm):	maxM
Max σ = σA(MPa):	maxσ
Max θ = θB (degrees)	maxθ
Max y = yA(mm):	maxY

If a=0 and wl = 0 (uniformly decreasing load)

Max M = MA(Nmm):	maxM
Max σ = σA(MPa):	maxσ
Max θ = θB (degrees)	maxθ
Max y = yA(mm):	maxY