"I'm sorry, Tiffania. Could you repeat what you just said to me?" Alexander said, taken aback by the wish her sister wanted him to do.
"I told you, I want you to tutor me about engineering, preferably everything you know about the subject," Tiffania repeated in a soft tone of voice.
So she's not really joking, she wanted him to become her tutor. Alexander hummed as he pondered about it. Well, if Tiffania wanted to, who is he to refuse? In fact, this is a good chance for them to bond together as brother and sister. But before he does so, he has to ask one important thing to her.
"Tiffania, I thought your specialty is in social studies? Social studies and Engineering is a completely different fields. What changed your mind?"
"Well, brother, I just think studying engineering is cooler than social studies as you can contribute more to the country. Didn't I tell you before, I was inspired to study engineering because of you."
Alexander was stunned momentarily at her heartfelt words. He smiled sweetly at her words as he appreciated them. If she's saying it this way, how can he refuse her?
"Your words somehow made me happy Tiffania. If it's what you want then I guess I'll have to. Now, there are a lot of different fields in engineering and the topic is broad. Is there any field that you're interested in?"
"Uhm...' Tiffania paused as she thought deeply about it. "Well...brother, what field are you most knowledgeable with?"
"Mechanical engineering," Alexander answered without hesitation. "I'm quite confident in that field."
"Ahh..." Tiffania mused as she somberly looked down.
Alexander tilted his head to the side, concerned as to what made her make that expression.
"Is something the matter?" Alexander asked, worriedly.
"Nope! Nothing's wrong, it's just that I was studying a different course." Tiffania quickly replied and smiled again to reassure him.
Alexander sighed and nodded his head in understanding. He looked down at his table where a document rested atop it. "So this document, are these some sort of a math problem?"
"Yes...but I don't think it is related to mechanical engineering," Tiffania flipped the front page of the document, allowing Alexander to peruse the contents. Alexander immediately recognized the topic.
"Ah...that's the analysis of trusses. It's true that it's not related to mechanical engineering. It's more on the civil engineering side. But don't worry, I'm familiar with the topic. So this is the one you want me to teach you about? Tiffania?"
Alexander's eyes narrowed when Tiffania was staring at him with her eyes widened.
"You know how to solve this, brother?" Tiffania stammered, surprised to hear Alexander knew how to solve the problem that is causing her headache.
"Of course, this one is fairly simple really. But to solve this, you must have knowledge in trigonometry, how to solve force vectors and moment of force."
"Eh? What is that, brother?" Tiffania furrowed her eyebrows, not understanding what his brother had mentioned.
"This is what I'm worried about," Alexander sighed. "The vector is a force that has both magnitude and direction. The moment of force, also known as torque, is a tendency for the body to rotate about a point that is not on the line of action of force. Moment of force can be calculated by multiplying force and distance," he explained. Tiffania listened closely with interest while her face lit up.
"Now those two are present in this truss problem, so let's try to solve it," Alexander's eyes shifted to the given problem in the document. "Find the force acting on all members of the truss shown below using the method of joints. There are two external forces. 50-kilonewton horizontal force at point C and 80 kilonewtons vertical at point F. This is a lot of members so I'm only going to show you how force AB is solved.
Tiffania nodded, her eyes already set on the problem.
"To get force AB, let's solve the moment at point D which will help us obtain the vertical force of the pin support of point A. Assume clockwise rotation is positive. So, 3Av plus 50 kilonewton multiplied by 1 meter equals 80 kilonewtons multiplied by 0.75 meters. Solve for Av we get…" Alexander wrote his solution on a blank sheet of paper. Five seconds later, he got the answer. "Av is equal to 3.33 kilonewton. Any question about how I got it?"
Tiffania nodded her head. "What do you mean by pin support?"
"Ah…there are three basic supports in the analysis of trusses, they are roller, pin, and a fixed support. Roller support only has a vertical reaction, pin support has a horizontal and vertical reaction, and fixed support has horizontal, vertical, and moment reactions. Point A is pin supported so it has two reaction forces. We just got a vertical reaction which is 3.33 kilonewton. Now we find horizontal force by using the summation of horizontal forces. Do you see any force acting on the trusses that are horizontal?"
Tiffania looked at the question carefully and she found it. "There, at point C, 80 kilonewtons to the right."
"Good and that's the answer," Alexander revealed.
"Eh? That's it? How? Explain it to me."
"Summation of Fh is Ah plus 80 kilonewtons. Transpose to the other side then we get negative 80 kilonewtons."
"But, brother, why is your answer positive despite it being negative?" Tiffania added.
"Positive and negative only indicate the direction of a force. Right is positive and left is negative. There's no negative value because the value of force can't be negative. Are you familiar with the third-newton law? That in every action, there is an equal and opposite reaction."
Hearing his explanation, Tiffania finally understood. Her brother is sure to be good at this. Making her feel ashamed of herself as she's the only one in the family who studies hard. Alexander has never been studious in the past, she never expected that her brother is going to outsmart her. There's only one explanation for this, his brother is a genius, and genius beats hard work.
"Please continue, brother," Tiffania requested.
"Well then. To solve force AB let's draw a free body diagram. The size of the horizontal plane is 1 meter while the vertical plane is 0.75 meters. Using the Pythagorean equation, we can determine the length of the longest side, which is the hypotenuse. The hypotenuse is equal to 1.25 meters. Now, we can solve for force AB. 0.75 divided by 1.25 multiplied by force AB is equal to 3.33 kilonewton. Divide both sides by 0.75/1.25, we get 5.55 kilonewton. Since we assumed that force Av is downward and we got a positive value, it means that the force is tensional."
Tiffania looked at his solution sheet, understanding what he did during the process. She couldn't help but feel amazement at her brother. He made it look so easy and despite her diving into the realm of mathematics, she understood it easily when her brother was explaining.
"Now, brother...please solve all the force members!" Tiffania said, her eyes beaming with excitement.
Alexander was smiling back at his beloved little sister. Time to surprise her again. Alexander cracked his knuckles and started scribbling equations on the sheet.
Tiffania watched as her brother solved one force to another. He was fast, very fast. It's like he knows what he is doing and how to calculate things effortlessly. She could barely take her eyes off him for she was mesmerized by his performance. When he finished solving all the problems, he was done. It just took him three minutes to solve. An average person could solve this problem in 15 to 30 minutes.
Tiffania was speechless as her mouth hung open slightly. Her brother is a hidden genius! And she wants to learn more about engineering topics from him. After a long time, she managed to recover herself from her astonishment. "Brother, that was brilliant!"
"Of course, it's required for someone like me to know these things. Do you think your brother can build amazing airplanes, vehicles, helicopters, appliances, and others without knowing math?" Alex asked smugly.
"Brother! Please teach me more!"
Alexander looked at his watch and his schedule for the day. "I'm free this morning so I guess I can
give you my time today. Is that okay?"
"That's great! Thank you, brother!" Tiffania exclaimed as she jumped happily toward her brother and gave him a tight hug.
Alexander was taken aback by her sudden actions. Four years ago she was kind of repulsive to him but now she has become more affectionate towards him than ever before. Alexander cherished this moment. And just as he could wrap her arm around her, she suddenly released herself. Her face flushed red as she just realized what she did.
She turned away from him and quickly ran out of the room. The sound of a door slamming against the wall followed shortly after.
"That's kind of sad," Alexander murmured. Does that mean she is taking back her words? He gazed down at the solution paper. Teaching her about things he is an expert on made him feel happy. "Well, I guess I have to return to work then."
