Question
Asked Nov 9, 2019

determine the reactions at the supports A and B, then draw the shear and moment diagrams. EI is constant.

A
L_
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A L_

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Step 1
Given information:
The length of the beam is L.
EI is constant
Calculation:
Sketch the Free Body Diagram of the beamas shown in Figure 1
wL
М
L
L
2
2
В,
Figure
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Given information: The length of the beam is L. EI is constant Calculation: Sketch the Free Body Diagram of the beamas shown in Figure 1 wL М L L 2 2 В, Figure

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Step 2
Refer to Figure 1
Find the support reaction as shown below
Apply the Equations of Equilibrium as shown below.
Summation of forces along horizontal direction is Equal to zero.
ΣΗ-0
F 0
A 0
Hence, the horizontal reaction at A is A 0.
Summation of forces along vertical direction is Equal to zero.
Ση-0
(1)
AyBy wL= 0
Take moment about A is Equal to zero.
ΣΜΑ
0
0 (2)
MABy x L- wL x
MA+B,L- 0
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Refer to Figure 1 Find the support reaction as shown below Apply the Equations of Equilibrium as shown below. Summation of forces along horizontal direction is Equal to zero. ΣΗ-0 F 0 A 0 Hence, the horizontal reaction at A is A 0. Summation of forces along vertical direction is Equal to zero. Ση-0 (1) AyBy wL= 0 Take moment about A is Equal to zero. ΣΜΑ 0 0 (2) MABy x L- wL x MA+B,L- 0

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Step 3
Sketch the Free Body Diagram of the beam at x distance from B as
shown in Figure 2
wx
Mx)
x
x
2
В,
Figure 2
Refer to Figure 2.
Take moment about the section as shown below.
М (") — В, х а — wx х
_
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Sketch the Free Body Diagram of the beam at x distance from B as shown in Figure 2 wx Mx) x x 2 В, Figure 2 Refer to Figure 2. Take moment about the section as shown below. М (") — В, х а — wx х _

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