はりの計算式(10) －境界条件部分載荷－

はりの計算式を連載で紹介しています。

境界条件部分載荷です。

支持条件

tp = 0 単純ばり

tp = 1 片持ち梁(自由固定)

tp = 2 片持ち梁(固定自由)

tp = 3 両端固定

tp = 4 １端ピン他端固定

tp = 5 １端固定他端ピン

の境界条件

qA = Q(x=0) せん断力

mA = M(x=0) 曲げモーメント

tA = T(x=0) たわみ角を曲げ剛性 EI で乗じたもの

vA = V(x=0) たわみを曲げ剛性 EI で乗じたもの

からはりを計算するやり方です。

計算式本体

境界条件

プログラム例

:境界条件部分載荷
@echo off
ruby -x %0
pause
goto:eof

#!ruby

# ｎ次分布荷重
def mq4(x, tp, l, a, c, n, w, ra, ma, ta, va, ei = nil, __g__ = 0)
b = l - a - c
n = n.abs
n1 = n + 1.0
n2 = n + 2.0
n3 = n + 3.0
n4 = n + 4.0

px = w * ( (x - a) / b) ** n * (x < a ? 0 : (x < a + b ? 1 : 0))
w = w * b / n1 * (x < a + b ? 0 : 1)
q = ra - px / n1 * (x - a) - w
m = ma + ra * x - px / (n1 * n2) * (x - a) ** 2 - w * b / n2 - w * (x - a - b)
t = ta - ma * x - ra / 2 * x ** 2 + px / (n1 * n2 * n3) * (x - a) ** 3 +
w * b ** 2 / (n2 * n3) + w * b / n2 * (x - a - b) + w / 2 * (x - a - b) ** 2
v = va + ta * x - ma / 2 * x ** 2 - ra / 6 * x ** 3 + px / (n1 * n2 * n3 * n4) * (x - a) ** 4 +
w * b ** 3 / (n2 * n3 * n4) + w * b ** 2 / (n2 * n3) * (x - a - b) +
w * b / (2 * n2) * (x - a - b) ** 2 + w / 6 * (x - a - b) ** 3 + __g__ * (m - ma) * l ** 2

if ei == nil
return q, m, t, v
else
return q, m, t / ei, v / ei
end
end

x = 2.5 #m
l = 5.0 #m
w = 10.0 #kN/m
e = 6.5 * 10**6 #kN/m2
t = 0.15 #m
h = 0.30 #m
n = 0
a = 0.0 #m
c = 0.0 #m
g = e/15 #kN/m2

tp = 0 #境界条件

nnn = n
b = l - a - c
ei = e * t * h ** 3 / 12
ga = g * t * h
__g__ = 1.2 * ei / ga / l ** 2

n = n.abs
n1 = n + 1.0
n2 = n + 2.0
n3 = n + 3.0
n4 = n + 4.0
if tp == 0
# o-----o
qa = w * b * ( (l - a) * n2 - b * n1) / (l * n1 * n2)
ma = 0.0
s1 = n1 * n2 * n3 * b ** 3
s2 = 3 * n1 * n2 * n4 * (a - l) * b ** 2
s3 = n1 * n3 * n4 * (3 * a ** 2 - 6 * l * a + 2 * l ** 2) * b
s4 = n2 * n3 * n4 * (a ** 2 - 3 * l * a + 2 * l ** 2) * a
ta = w * b * (s1 + s2 + s3 + s4) / (6 * n1 * n2 * n3 * n4 * l)
va = 0.0
elsif tp == 1
# ------|
qa = 0.0
ma = 0.0
u1 = n1 * n2 * b ** 2
u2 = 2 * (a - l) * n1 * n3 * b
u3 = n2 * n3 * (a ** 2 - 2 * l * a + l ** 2)
ta = -w * b * (u1 + u2 + u3) / (2 * n1 * n2 * n3)
s1 = n1 * n2 * n3 * b ** 3
s2 = 3 * n1 * n2 * n4 * a * b ** 2
s3 = 3 * n1 * n3 * n4 * (a ** 2 - l ** 2) * b
s4 = n2 * n3 * n4 * (a ** 3 - 3 * l ** 2 * a + 2 * l ** 3)
s5 = 6 * ( (l - a) * n2 - b * n1) * n3 * n4 * l ** 2 * __g__
va = w * b * (s1 + s2 + s3 + s4 + s5) / (6 * n1 * n2 * n3 * n4)
elsif tp == 2
# |------
qa = w * b / n1
ma = -w * b * (b * n + a * n + b + 2 * a) / (n1 * n2)
ta = 0.0
va = 0.0
elsif tp == 3
# |-----|
u1 = n2 * n3 * n4 * (3 * (a + b) + c) * c ** 2
u2 = 6 * n4 * (c * n2 + a) * b ** 2
u3 = 6 * n3 * n4 * a * b * c
u4 = 6 * n2 * b ** 3
u5 = 12 * ( (l - a) * n2 - b * n1) * n3 * n4 * __g__ * l ** 2
qa = w * b * (u1 + u2 + u3 + u4 + u5) / (l ** 3 * (12 * __g__ + 1) * n1 * n2 * n3 * n4)
s1 = (a * n2 + b * n1) * n3 * n4 * c ** 2
s2 = 2 * (a + c * n1) * n4 * b ** 2
s3 = 2 * n3 * n4 * a * b * c
s4 = 2 * n1 * b ** 3
s5 = 6 * l * ( (b * (c * n1 + a) + a * c * n2) * n3 + b ** 2 * n1) * n4 * __g__
ma = -w * b * (s1 + s2 + s3 + s4 + s5) / (l ** 2 * (12 * __g__ + 1) * n1 * n2 * n3 * n4)
ta = 0.0
va = 0.0
elsif tp == 4
# o-----|
u1 = n1 * n2 * n3 * b ** 3
u2 = 3 * n1 * n2 * n4 * a * b ** 2
u3 = 3 * n1 * n3 * n4 * b * (a ** 2 - l ** 2)
u4 = n2 * n3 * n4 * (a ** 3 - 3 * l ** 2 * a + 2 * l ** 3)
u5 = 6 * n3 * n4 * ( (l - a) * n2 - b * n1) * __g__ * l ** 2
qa = w * b * (u1 + u2 + u3 + u4 + u5) / (2 * l ** 3 * (3 * __g__ + 1) * n1 * n2 * n3 * n4)
ma = 0
s1 = n1 * n2 * n3 * b ** 3
s2 = n1 * n2 * n4 * (3 * a - 2 * l) * b ** 2
s3 = n1 * n3 * n4 * (3 * a ** 2 - 4 * l * a + l ** 2) * b
s4 = n2 * n3 * n4 * (a ** 2 - 2 * l * a + l ** 2) * a
s5 = 6 * ( (n1 * b * (l - 2 * a) + n2 * a * (l - a)) * n3 - b ** 2 * n1 * n2) * n4 * l * __g__
ta = w * b * (s1 + s2 + s3 + s4 + s5) / (4 * l * (3 * __g__ + 1) * n1 * n2 * n3 * n4)
va = 0
elsif tp == 5
# |-----o
u1 = n1 * n2 * n3 * b ** 3
u2 = 3 * n1 * n2 * n4 * (a - l) * b ** 2
u3 = 3 * n1 * n3 * n4 * (a - 2 * l) * a * b
u4 = n2 * n3 * n4 * (a ** 3 - 3 * l * a ** 2 + 2 * l ** 3)
u5 = 6 * (l * n2 - (a + b) * n1) * n3 * n4 * l ** 2 * __g__
qa = w * b * (u1 + u2 + u3 + u4 + u5) / (2 * l ** 3 * (3 * __g__ + 1) * n1 * n2 * n3 * n4)
s1 = n1 * n2 * n3 * b ** 3
s2 = 3 * n1 * n2 * n4 * (a - l) * b ** 2
s3 = n1 * n3 * n4 * (3 * a ** 2 - 6 * l * a + 2 * l ** 2) * b
s4 = n2 * n3 * n4 * (a ** 2 - 3 * l * a + 2 * l ** 2) * a
ma = -w * b * (s1 + s2 + s3 + s4) / (2 * l ** 2 * (3 * __g__ + 1) * n1 * n2 * n3 * n4)
ta = 0
va = 0
end

if nnn > 0
q, m, t, v = mq4(x, tp, l, a, c, n, w, qa, ma, ta, va, ei, __g__)
p [x, q, m, t, v]
else
q, m, t, v = mq4(l - x, tp, l, c, a, -n, w, qa, ma, ta, va, ei, __g__)
p [x, -q, m, -t, v]
end

__END__