fundamentals of engineering supplied-reference handbook - Ventech!

STRUCTURAL ANALYSIS
Influence Lines
An influence diagram shows the variation of a function
(reaction, shear, bending moment) as a single unit load
moves across the structure. An influence line is used to (1)
determine the position of load where a maximum quantity
will occur and (2) determine the maximum value of the
quantity.
Deflection of Trusses
Principle of virtual work as applied to trusses
∆ = ΣfQδL
∆ = deflection at point of interest
fQ = member force due to virtual unit load applied at
the point of interest
δL = change in member length
= αL(∆T) for temperature
= FpL/AE for external load
Pab
2
FEM AB =
L
2
FEM AB =
FEM AB =
BEAM FIXED-END MOMENT FORMULAS
wo
2
L
12
wo
2
L
30
114
CIVIL ENGINEERING (continued)
α = coefficient of thermal expansion
L = member length
Fp = member force due to external load
A = cross-sectional area of member
E = modulus of elasticity
∆T = T–TO; T = final temperature, and TO = initial
temperature
Deflection of Frames
The principle of virtual work as applied to frames:
⎧ L mM ⎫
∆ = ∑⎨∫
dx
O ⎬
⎩ EI ⎭
m = bending moment as a function of x due to virtual
unit load applied at the point of interest
M = bending moment as a function of x due to external
loads
Pa
2
b
FEM BA =
L
2
FEM BA =
FEM BA =
Live Load Reduction
The live load applied to a structure member can be reduced as the loaded area supported by the member is increased. A typical
reduction model (as used in ASCE 7 and in building codes) for a column supporting two or more floors is:
⎛
Lreduced = L ⎜
nominal 0.25 +
⎜
⎝
15
kLL
AT
⎞
⎟ ≥ 0.4 Lnominal
⎟
⎠
Columns: kLL = 4
Beams: kLL = 2
where Lnominal is the nominal live load (as given in a load standard or building code), AT is the cumulative floor tributary area
supported by the member, and kLL is the ratio of the area of influence to the tributary area.
wo
2
L
12
wo
2
L
20