USES OF LAW OF TRIGONOMETRY IN STRUCTURAL DESIGN

Many student in primary school especially science student frequently ask why we learn sine,cosine,tangent,cosec,sec and cotangent in the math subject.To remember the law and formula without knowing where and when to use these kind of formulae.

The authors have a lot of example from the structural design whose all the law very useful in design  of shear stress or strength of the element like wall,beam,column,slab,pile cap and truss for roofing.Let we go first example when we want to find a nominal shear strength for shear wall

• Shear wall-nominal shear strength
• Vrd,max=∝wbwzv1∱ed(Cot Θ +tanΘ)
• Vrd,s=Asw/s(zfywd CotΘ)
• K(tie and strur)=-D+Fh/(CosΘ +Fv/SinΘ) +1/(-D +Fh/(cosΘ)*(1-Sin^2Θ/2)+Fv/(Sin Θ)*(1-Cos^2Θ/2) > 1.0
• ժv=ժd Sin^2Θ +Cos^2Θ +ρvfv
• ժh=ժd Cos^2(Θ) +ժrSin^2(Θ) + pufu
• τvh=(ժr-ժd)SinΘCosΘ
• Θ=Sin ^-1*((-ժv +ժr + pvfv)/(-ժd +ժr))^0.5
• Vn=(ժr-ժd)SinΘCosΘtwdw +1.64befbbe((fc'))^3.2
• Beam theory-shear reinforcemet
• Pile Cap Shear Reinforcement
• Deep beam
• Corbel
• Roofinf truss system

In the soil mechanic

• Mohr-coulumb formulae ፒ= c +Ժ tanΦ
• Stress Ժ=Ժ1+tan ^2*(45 -Φ/2)- 2ctan(45-Φ/2)
• F for slope stability Σ(c'△X੬c∝ + tanΦ('(wcos∝ +u△Xsec(x))/Σ(wsin∝)

There are a few example from thousands of equation using the sine,cosine and other of trigonometry formulae.Today with a engineering software from 2D image until to the 3D image and model,all the formulae are hidden and not exposed to the student.All the engineering student only know and understand the basic of that formulae.If we can understand very good,all the student can expand and make a new innovation in engineering product, base on that basic formulae.