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Structural Question regarding beam analysis: Deflections and advanced analysis Document Preview: Question 10.1 The following diagram shows a three pin frame loaded with 6kN roof dead loads at each...

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Structural Question regarding beam analysis: Deflections and advanced analysis
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Question 10.1 The following diagram shows a three pin frame loaded with 6kN roof dead loads at each purlin. The frame has pins at A, E and I. The knee joints at C and G are rigid joints (that is they are capable of transferring bending moments). 4x1.5m =6m 4m A I C D E F G 4kN 4kN 4kN 4kN 4kN Determine the support reactions at the pin joints A, E and I for the following three pin frame and determine the bending moment at the knees at C and at G. Also determine the shear in the horizontal beams just next to the knee joints. Place half the 4kN load at E on each side of the hinge at E. Fig 10.27 Answers: MC = MG = -12kN.m VC+ = +6kN VG- = -6kN Ay = Iy = 10kN Ax = +3kN; Ix = -3kN E’x = -3kN; E”x = +3kN; E’y = E”y = 0kN Question 10.2 The following diagram shows the same three pin frame analysed in the previous workbook question and in the earlier worked example. The load case shown in the diagram includes only the sideways wind loads applied to the building. (The same sideways loads were analysed in the earlier worked example but that load case included uplift on the roof, this load case does not include uplift. As before, the frame has pins at A, D and G. The knee joints at B and F are rigid joints (that is they are capable of transferring bending moments). Determine the support reactions at the pin joints A, D and G for the following three pin frame and determine the bending moment at the knees at C and at F. Also determine the shear in the horizontal beams just next to the knee joints. 4x1.5m =6m 2x2m=4m B 5kN H C D E F G 5kN 10kN 3kN 3kN 6kN A I Fig 10.28 Answers: MC+ = +32kN.m; MG- = -32kN.m VC+ = -10.67kN VG- = -10.67kN Ay = -10.67; Iy = +10.67kN Ax = -18kN; Ix = -14kN D’x = -2kN; D”x = +2kN; D’y = +10.67kN; D”y = -10.76kN

Answered Same Day Dec 21, 2021

Solution

David answered on Dec 21 2021
121 Votes
Question 10.1
The following diagram shows a three pin frame loaded with 6kN roof dead loads at each
purlin. The frame has pins at A, E and I. The knee joints at C and G are rigid joints (that
is they are capable of transfe
ing bending moments).
Determine the support reactions at the pin joints A, E and I for the following three pin
frame and determine the bending moment at the knees at C and at G. Also determine
the shear in the horizontal beams just next to the knee joints. Place half the 4kN load at
E on each side of the hinge at E.
Fig 10.27
Answers:
MC = MG = -12kN.m
VC+ = +6kN
VG- = -6kN
Ay = Iy = 10kN
Ax = +3kN; Ix = -3kN
E’x = -3kN; E”x = +3kN; E’y = E”y = 0kN
From Fig.1, we can observe that the structure is symmetrical (both in terms of loading
as well as in terms of geometry). So, we have RAy = RIy = (4*5)/2 = 10kN (acting
upwards)
Also, RAx = RIx ....(1)
Next refer Fig.2. As joint E is pinned, so M = 0. Now, take moments of forces about joint
E. We have,
RAx *4 + 4*3 + 4*1.5 = RAy*3
=> Rax*4 + 18 = 10*3
=> RAx = 3kN (acting towards right)
Now, RIx = RAx as per eqn.(1) above.
So, RIx = 3kN (acting towards left, refer Fig. 1 for direction). With...
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