M (kN.m) e. V (kN) A cantilevered beam has of length L = 10 m and is subjected to a vertical load P₁ = 50 kN, an axial load P₂ = 100 kN passing through the neutral axis, a moment M = 200 kN.m, and a uniformly distributed load w = 30 kN/m, as shown. The cross-sectional view and dimensions are illustrated below, with point C representing the centroid of the cross-section. 300 mm W P₁ ولا 25 mm Neutral Axis 200 mm A x D P2 M Support Material 50 mm STRESS FORMULATION 25 mm N 2 Normal stress: σN= Beam's cross-section M₂y L (m) Bending stress: Τρ Torsional shear stress: T= d. Draw the shear force diagram for the beam. Show all your work. V, Q Transverse shear stress: T= Q=YA' or Q= P W 1₂t BEAM SIGN CONVENTION V V ty w L(m) Neutral Axis Pz M (w): Positive internal shear M M Positive internal moment Beam sign convention CROSS-SECTIONAL MOMENTS OF INERTIA ABOUT THE CENTROID y bh³ Quadratic (second) 1, = l₁ = moment of inertia 12 hb3 12 πρ 1₂ = ly=4 Polar moment of inertia 1x = bh3+hb3 12 πρ Draw the bending moment diagram for the beam. Show all your work. P₁ Centroid location: Parallel axis theorem: Σχιλι = Al 1c ==Σ (1c₁ + A₁ d₁²) A L 42 D L (m) Neutral Axis P₂ M x (m)
M (kN.m) e. V (kN) A cantilevered beam has of length L = 10 m and is subjected to a vertical load P₁ = 50 kN, an axial load P₂ = 100 kN passing through the neutral axis, a moment M = 200 kN.m, and a uniformly distributed load w = 30 kN/m, as shown. The cross-sectional view and dimensions are illustrated below, with point C representing the centroid of the cross-section. 300 mm W P₁ ولا 25 mm Neutral Axis 200 mm A x D P2 M Support Material 50 mm STRESS FORMULATION 25 mm N 2 Normal stress: σN= Beam's cross-section M₂y L (m) Bending stress: Τρ Torsional shear stress: T= d. Draw the shear force diagram for the beam. Show all your work. V, Q Transverse shear stress: T= Q=YA' or Q= P W 1₂t BEAM SIGN CONVENTION V V ty w L(m) Neutral Axis Pz M (w): Positive internal shear M M Positive internal moment Beam sign convention CROSS-SECTIONAL MOMENTS OF INERTIA ABOUT THE CENTROID y bh³ Quadratic (second) 1, = l₁ = moment of inertia 12 hb3 12 πρ 1₂ = ly=4 Polar moment of inertia 1x = bh3+hb3 12 πρ Draw the bending moment diagram for the beam. Show all your work. P₁ Centroid location: Parallel axis theorem: Σχιλι = Al 1c ==Σ (1c₁ + A₁ d₁²) A L 42 D L (m) Neutral Axis P₂ M x (m)
Principles of Foundation Engineering (MindTap Course List)
8th Edition
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Chapter6: Vertical Stress Increase In Soil
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Problem 6.4P: Refer to Figure P6.4. A strip load of q = 900 lb/ft2 is applied over a width B = 36 ft. Determine...
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Transcribed Image Text:M (kN.m)
e.
V (kN)
A cantilevered beam has of length L = 10 m and is subjected to a vertical load P₁ = 50 kN, an axial
load P₂ = 100 kN passing through the neutral axis, a moment M = 200 kN.m, and a uniformly
distributed load w = 30 kN/m, as shown. The cross-sectional view and dimensions are illustrated
below, with point C representing the centroid of the cross-section.
300 mm
W
P₁
ولا
25 mm
Neutral Axis
200 mm
A
x
D
P2
M
Support Material
50 mm
STRESS FORMULATION
25 mm
N
2
Normal stress:
σN=
Beam's cross-section
M₂y
L (m)
Bending stress:
Τρ
Torsional shear stress:
T=
d.
Draw the shear force diagram for the beam. Show all your work.
V, Q
Transverse shear stress:
T=
Q=YA'
or
Q=
P
W
1₂t
BEAM SIGN CONVENTION
V
V
ty
w
L(m)
Neutral Axis
Pz
M
(w):
Positive internal shear
M M
Positive internal moment
Beam sign convention
CROSS-SECTIONAL MOMENTS OF INERTIA ABOUT THE CENTROID
y
bh³
Quadratic (second)
1, =
l₁ =
moment of inertia
12
hb3
12
πρ
1₂ = ly=4
Polar moment of
inertia
1x =
bh3+hb3
12
πρ
Draw the bending moment diagram for the beam. Show all your work.
P₁
Centroid location:
Parallel axis theorem:
Σχιλι
= Al
1c ==Σ (1c₁ + A₁ d₁²)
A
L
42
D
L (m)
Neutral Axis
P₂
M
x (m)
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