Om ang g caT VI CIO nPPOTcd Uy ImI an Uports a 42 kips load at Point B (midway between Pin A and Roller C).at Pin A (0A), the deflection at Point B (AB), the slope at Point D Cat Point D (AD). The beam has the following properties: E 10,0042k15FT15r12 FTer beam shown below has length L, and a fixed support at the left eniformly distributed load (w) at the free end. The distributed loafrom the fixed end. Determine the formulas for formulas for 0of the cantilever beam. [Note: Just like the formulas inside thefunction of w L a Eand I.1.+hese fo ues. he

Question
Asked Oct 11, 2019

The 42 foot long overhanging beam shown is supported by a pin at A and a roller at C. The beam supports a point load of 42 kips at point B. Determine the slope at pin A, deflection at point B, and the slope and deflection at point D. Modulus of Elasticity, E = 10,000ksi, Moment of Inertia, I = 2500in4.

Let slope and deflection be functions of x, with x positive to the right.

Om ang g caT VI CIO nPPOTcd Uy ImI an U
ports a 42 kips load at Point B (midway between Pin A and Roller C).
at Pin A (0A), the deflection at Point B (AB), the slope at Point D C
at Point D (AD). The beam has the following properties: E 10,00
42k
15FT
15r
12 FT
er beam shown below has length L, and a fixed support at the left e
niformly distributed load (w) at the free end. The distributed loa
from the fixed end. Determine the formulas for formulas for 0
of the cantilever beam. [Note: Just like the formulas inside the
function of w L a Eand I.1.
+hese fo ues. he
help_outline

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Om ang g caT VI CIO nPPOTcd Uy ImI an U ports a 42 kips load at Point B (midway between Pin A and Roller C). at Pin A (0A), the deflection at Point B (AB), the slope at Point D C at Point D (AD). The beam has the following properties: E 10,00 42k 15FT 15r 12 FT er beam shown below has length L, and a fixed support at the left e niformly distributed load (w) at the free end. The distributed loa from the fixed end. Determine the formulas for formulas for 0 of the cantilever beam. [Note: Just like the formulas inside the function of w L a Eand I.1. +hese fo ues. he

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Expert Answer

Step 1
Step 2
Showthe free body diagram ofthe overhanging beamas shownbelow
42k
ो
н;
15 ft
12 ft
15 ft
Figure
Referthe above Figure.
Find the support reactions atA and C.
Apply Equilibrium Equation
Take the sum ofthe forces in the horizontal direction as zero.
ΣΕ-0
H 0
There is no loadin the overhangingportion ofthe beamand the loadingis symmetric
overthe portionAC ofthe beam Then,
42kip
V=Vc=2
V4-Vc=21kip
help_outline

Image Transcriptionclose

Showthe free body diagram ofthe overhanging beamas shownbelow 42k ो н; 15 ft 12 ft 15 ft Figure Referthe above Figure. Find the support reactions atA and C. Apply Equilibrium Equation Take the sum ofthe forces in the horizontal direction as zero. ΣΕ-0 H 0 There is no loadin the overhangingportion ofthe beamand the loadingis symmetric overthe portionAC ofthe beam Then, 42kip V=Vc=2 V4-Vc=21kip

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Step 3
Consider a section at a distance x from.A in the region AB.
Calculate the moment at the sectionxand apply the double integration method.
M(x)Vx
м (х) -21х
EIY
M(x)
EI
- 21x
cx
21x
EI
2
21x
+CxC
6
Еly
Apply the boundary conditions to calculate the constants.
The deflection is zero atthe supportA, thatis at -0 thevalue ofy-0.
The deflection is zero atthe support B, that is atx-30 the value ofy 0.
21(0)
+G(0)+ C
6
вI(0) -
12in
21 30ftx
1ft
12in
EI(0)=
+0
30ftx
+
6
1ft
0 163296,000+3 60 C
163296, 000
360
G-453,600
n
help_outline

Image Transcriptionclose

Consider a section at a distance x from.A in the region AB. Calculate the moment at the sectionxand apply the double integration method. M(x)Vx м (х) -21х EIY M(x) EI - 21x cx 21x EI 2 21x +CxC 6 Еly Apply the boundary conditions to calculate the constants. The deflection is zero atthe supportA, thatis at -0 thevalue ofy-0. The deflection is zero atthe support B, that is atx-30 the value ofy 0. 21(0) +G(0)+ C 6 вI(0) - 12in 21 30ftx 1ft 12in EI(0)= +0 30ftx + 6 1ft 0 163296,000+3 60 C 163296, 000 360 G-453,600 n

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