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**Unformatted text preview: **Determine the reactions at A and B.
(c) Draw the shear force and bending moment diagrams, labeling all critical values.
P B C k A
L L/2 Figure 4 Name: Signature:
Student Number: Information Sheet for CIVL 230 Exam
Stresses and Strains
ε = δ / L; γ = δ s / h; σ = P / A; τ = V / As bg σ = Eε ; τ = Gγ ; G = E / 2 1 + ν Axial Bar
PL
; displacement of a uniform bar under uniform load
AE
LN x
δ=
dx ; displacement of a non - unifom bar under non - uniform load N x
0
EA δ= z bg bg
displacement due to non - uniform temperature change ∆T b x g δT = z U= 1 P2 L
; strain energy of a uniform bar
2 AE L 0 bg α ∆T x dx ; Torsional Bar
T τ Gϕ
==
; torsion formula for a uniform bar under uniform torque T
Jr
L
γL = ϕr ; relation between shear strain γ and angle of twist ϕ πR 4
J=
; polar 2nd moment of area for a solid circular section of radius R
2
LT x
ϕ=
dx ; twist at the end of a non - uniform bar of length L under non - uniform torque T x
0 GJ z bg bg Beam Bending
y
ρ
M
σE
= − = ; bending stress formula for a homogeneous beam
I
yρ ε = − yκ = − bh3
; 2nd moment of area of a rectangular section beam about the z axis
12
M Ei y
σi = −
; bending stress in material i for a composite beam
å Ei Ii
I= i dM
; shear - moment relation
dx
VQ
f=
; shear flow with Q = y dA ; 1st moment of area about the z axis
I
A V= z d 2v M
=
; differential equation for beam deflection v
dx 2 EI Name: Signature:
Student Number: Information Sheet for CIVL 230 Exam
Beam Deflections...

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