Solution to Questions of the Week (4th week, May, 2018) and Winners

Earlier this week, I started the daily questions program on Structville and I am happy for the kind of the reception the program has received. We are going to summarise the all questions asked last week, provide solution to the questions, and recognise those who participated.

Wednesday 23 May, 2018
We were asked to determine the equation that the two beams shown below have in common in their final state. The question has the conditions of assuming linear elastic response.

Solution
We can see that the difference in the beams is based on their support conditions. The first beam is simply supported, while the second beam is fully fixed at the supports. Under the action of the externally applied uniformly distributed load, the simply supported beam develops a maximum sagging moment of wL²/8 which occurs at the mid-span. However, the shear force at the support remains wL/2.

In the free state, the second beam develops a maximum sagging moment of wL²/8 which occurs at the mid-span, and a hogging fixed end moment of wL²/12 which occurs at the support. Now in the final state (combining free moment and fixed end moment), the maximum sagging moment becomes  wL²/8 – wL²/12 = wL²/24 (at the midspan). But the shear force remains wL/2. So the correct answer is D.

Those who got the answer correct are:

• Ogungbire Adedolapo
• Palo Tuleja
• Nitesh Mithapelli

Thursday, 24 May, 2018
We were required to determine the support reaction and bending moment at support C of the compound beam loaded as shown below;

Bending Moment at Support C
The bending moment at support C can be expressly determined by considering the cantilever moment from the concentrated load at the free end of the overhang.

M_C^R = -2 kN × 2m = -4 kN.m

Support Reaction at Support C
There are two easy ways of obtaining the vertical reaction at support C.
Since the values of the reaction at A and B are already given, we can easily sum up the vertical forces. (upward forces positive, downward forces negative)

Hence
 -2 – (6 × 4) – 2 + 1 + 34.6 – Cy = 0
Cy – 7.6 = 0
Cy = 7.6 kN (downwards)

On the other hand, we can take moment about point G just to the left. But Structville question is designed so that very simple approaches can be used to obtain the answers. So the correct answer is C.

The people that got the answers correct are as follows:

• Ogungbire Adedolapo
• Ovie Agbaga
• Theodoros Gianneas
• Subramanian Narayanan
• Peter O.

Friday 25 May, 2018
In this one, we are required to obtain the bending moment just to the left of point E and the horizontal support reaction at support B.

To obtain the moment just to the left of node E, we have to carry out a very simple calculation. The support reaction at support A has already been provided.

Hence;
M_G^L = (2 × 4) – (2 × 4²)/2 = – 8kNm
This is just as simple as that.

The horizontal support reaction can be readily obtained by summing up the horizontal forces. All forces pointing towards the right are taken as positive, while forces pointing towards the left is taken as negative.

Therefore;
4 kN – 7 kN + 4.875 kN – Bx = 0
1.875kN – Bx = 0
Bx = 1.875 kN

Therefore the correct answer is C.

The people that got the answer correct are;

• Thaddeus Odinakachi Ekwugha
• Ogungbire Adedolapo

My sincere appreciation also goes to all the people who commented on various social platforms. However for your response to be recognised specially, you must post it on this blog. Some people also commented on the blog anonymously. Thank you so much for your contributions. Let us look forward to this weeks questions. God bless.