Fo Compressed L KHHL F3 = ½ka (rst-w) H² L F WHIL Fs = Kaq (H, + H₂) L F is located at y = H₂+ H₁/3 from bottom H₂ F₂ is located at y = 2 Fs is located at y = H2/3 Fig 4 M F Hr.9' Y-120 pef Ka-0.32 Ka=0.32 F3 Fa YwH₂ kaq Каун Ka (s-Ya) Hz Fig 5 - Lateral earth pressure forces, live load surcharge forces 4 B T 4 NI F2 q A Kad H," F4 Y 13 C जा Fs F4 is located at y = Hz/3 Fs is located at y = (H₁ + H₂)/2 қан, Ka (8-8) H2 Fig 6- Equations for lateral earth pressure forces and live load surcharge forces Fs The plan and 3D elevation of an earth retaining structure used for support excavation is shown in Figs. 3 and 4 respectively. The retaining structure is made of wood planks supported in the horizontal direction on vertical steel piles (HP sections). The HP piles shape of an H and are typically used for piles. The section properties of these sections (A, I, S, etc...) are given in Part 1 of the AISC steel manual. The spacing of the supporting HP piles is 20ft. The height of the piles is 15 from top of the pile to top of the footing. The height of the water table from the top of the footing is 9 ft as shown in the elevation in Fig. 4. The pile height and soil properties and the earth pressure distribution behind the retaining structure are shown in Fig. 5. Figs. 6 shows the equations for earth pressure. q is a live load surcharge that accounts for traffic on top of the embankment; q is typically assumed to be 250 psf (per the bridge code (AASHTO)). Use Fy = 50 ksi Required 1. Determine the maximum horizontal force at the bottom of a typical interior HP pile due to lateral earth pressures and the live load on top of the embankment. 2. Determine the maximum moment at the bottom of a typical interior HP pile due to lateral earth pressures and the live load on top of the embankment. 3. If the maximum stress due to bending at the bottom of a typical interior HP pile cannot exceed 0.66Fy, what should be the minimum required section modulus Sx of the HP pile? What is the lightest HP pile that can be used? 4. If the maximum stress due to shear at the bottom of a typical interior HP pile cannot exceed 0.3Fy, what should be the minimum required web area (dx tw) of the HP pile? 5. What will be the factored LRFD horizontal force and bending moment? (use the values obtained from parts 1 and 2 and use load factor of 1.6 for earth pressure and 1.75 for live load). 6. If the section used was HP16x162, what would the deflection at top of pile? 20' Zo' 20' Zo' wood plank typical HP interior pile ४ = 120 pcf (16/ft³) Ka= 0.32 You Mo pef? Saturated soil 140 Ka= 0.32 Fig 3 - PLAN

The plan and 3D elevation of an earth retaining structure used for support excavation is  
shown in Figs. 3 and 4 respectively. The retaining structure is made of wood planks  
supported in  the horizontal direction on vertical steel piles (HP sections). The HP piles shape  
of an H and are typically used for piles. The section properties of these sections (A, I, S,  
etc…) are given in Part 1 of the AISC steel manual. The spacing of the supporting HP piles is  
20ft. The height of the piles is 15 from top of the pile to top of the footing. The height of the  
water table from the top of the footing is 9 ft as shown in the elevation in Fig. 4. The pile  
height and soil properties and the earth pressure distribution behind the retaining structure are  
shown in Fig. 5. Figs. 6 shows the equations for earth pressure. q is a live load surcharge that  
accounts for traffic on top of the embankment; q is typically assumed to be 250 psf (per the  
bridge code (AASHTO)).  Use Fy = 50 ksi 

1. Determine the maximum horizontal force at the bottom of a typical interior HP pile due 
to lateral earth pressures and the live load on top of the embankment.  
2. Determine the maximum moment at the bottom of a typical interior HP pile due to lateral 
earth pressures and the live load on top of the embankment.  
3. If the maximum stress due to bending at the bottom of a typical interior HP pile cannot 
exceed 0.66Fy, what should be the minimum required section modulus Sx of the HP pile? 
What is the lightest HP pile that can be used?  
4. If the maximum stress due to shear at the bottom of a typical interior HP pile cannot 
exceed 0.3Fy, what should be the minimum required web area (d x tw) of the HP pile?  
5. What will be the factored LRFD horizontal force and bending moment? (use the values 
obtained from parts 1 and 2 and use load factor of 1.6 for earth pressure and 1.75 for live 
load).  
6. If the section used was HP16x162, what would the deflection at top of pile?